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JOSEPH  A,  HOFMANN, 

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UNIVERSITY   OF   CALIFORNIA 

LIBRARY 

OF  THE 


Accessions  Afo...^.-2'..o...  Book  No.. .£.... 


NATUKAL 


PHILOSOPHY 


BY 

ISAAC  SHARPLESS,  Sc.D., 

PROFESSOR   OF    MATHEMATICS    AND    ASTRONOMY    IN    HAVERFORD    COLLEGE, 


AND 


GEO.  MORRIS   PHILIPS,  PH.D., 

PRINCIPAL   OF   STATE    NORMAL    SCHOOL,    WEST    CHESTER     PA. 


**-*? 


JTf 


o* 


PHILADELPHIA: 
J.  B.  LIPPINCOTT   COMPANY. 


JOSEPH  A.  HOFMANN, 

Bookseller  &  Stationer, 

208  MONTCOMERY  ST.. 
San  Francisco,  Cal. 


, 


Copyright,  1883,  by  J.  B.  LIPPINCOTT  &  Co. 


PREFACE. 


THIS  Treatise  on  Natural  Philosophy  differs  from  others 
in  the  large  number  of  practical  experiments  and  exercises 
which  it  contains.  The  authors  believe  that  students  of 
science  should  be,  as  far  as  possible,  investigators,  and,  to 
encourage  the  spirit  of  research,  they  have  given  sugges- 
tions tending  to  lead  them  on  in  this  way.  The  experi- 
ments can  nearly  .all  be  performed  with  very  simple  and 
inexpensive  materials,  such  as  any  school  or  home  can 
furnish.  More  elaborate  instruments  are  described  for  the 
benefit  of  classes  which  have  access  to  them.  The  book 
can  also  be  used  by  classes  which  have  not  time  to  perform 
the  experiments.  Yet  it  is  strongly  recommended  that  as 
many  as  possible  be  tried. 

Two  sizes  of  type  are  used  through  the  book.  The 
matter  printed  in  large  type  will  form  a  complete  ele- 
mentary course,  and  the  whole  book  a  more  exhaustive 
one.  Those  who  take  the  former  are  advised  to  include 
as  many  as  convenient  of  the  experiments,  exercises,  and 
questions.  The  large  number  given  will  allow  the  teacher 
to  make  selections  suited  to  the  ability  of  the  class. 

The  use  of  technical  terms,  except  where  they  seemed 
necessary  to  the  better  comprehension  of  the  subject,  has 
been  avoided.  It  has  been  recognized  that  the  majority 

673234  3 


PREFACE. 


of  students  of  natural  philosophy  have  no  use  for  these 
terms.  What  they  want  is  a  practical  knowledge  of  the 
subject  and  the  cultivation  of  scientific  habits  of  mind. 

The  methods  of  the  leading  scientific  men  of  the  present 
time  have  been  incorporated,  and  their  instruments  de- 
scribed and  figured.  In  any  treatise  on  the  subject  which 
embraces  an  account  of  these  methods,  the  doctrine  of  the 
conservation  of  energy  must  have  a  prominent  place.  The 
great  advances  in  practical  science  within  the  last  few 
years,  especially  in  sound,  electricity,  and  meteorology, 
have  also  been  utilized  so  far  as  they  seem  to  bear  on  the 
principles. 

The  work  has  been  greatly  benefited  by  the  criticisms 
and  suggestions  of  C.  Canby  Balderston,  of  Westtown 
School,  Pennsylvania.  The  chapters  on  Magnetism  and 
Electricity  were  written  by  him. 


CONTENTS. 


PREFACE     3 

CHAPTER  I.— Matter 7 

II.— Motion  and  Force 19 

Gravity  and  Stability 35 

Falling  Bodies 40 

The  Pendulum 44 

Machines  ........  47 

III.— Liquids 63 

Hydrostatics  .  .  .  .  .  .  .63 

Specific  Gravity 78 

Hydraulics 83 

Water-Machines 87 

IV.— Gases 95 

The  Atmosphere 100 

Pneumatic  Machines  .....  103 

V.— Sound 120 

Cause  and  Phenomena  .....  120 

Musical  Sound 129 

Musical  Instruments 133 

Music 150 

VI.— Light 162 

Keflection 169 

Refraction 177 

Dispersion 188 

Polarization  .......  202 

Optical  Instruments 205 

VII.— Heat 213 

Conduction 234 

Convection 236 

Steam-Engine 237 

VIII.— Magnetism 244 

1*  5 


CONTENTS. 


PAGE 

CHAPTER  IX.— Electricity 255 

Fractional  Electricity 255 

Current  Electricity 277 

Electro-Magnetism  .  .  .  .  .289 

Magneto-Electricity 304 

Kadiant  Matter 313 

X.— Meteorology 319 

The  Atmosphere 322 

APPENDIX  I.— The  Metric  System 343 

II.— Table  of  Specific  Gravities  .  .  .  .345 

INDEX  346 


NATURAL   PHILOSOPHY. 


CHAPTEE   I:        ,     ,,„ 

v,  >B  /,•  '     i  j..       ,'-.-:•' 

MATTER. 

1.  What  is  Matter? — All  the  bodies  which  occupy  space, 
the   stars   and   the   planets,   rocks,   water,   and   air,   and 
everything  we  can  see  or  feel,  are  embraced  under  the 
term  matter. 

We  can  crumble  a  rock  or  divide  a  quantity  of  water 
into  smaller  portions.  These  can  again  be  subdivided,  and 
all  the  fragments  will  resemble  the  original  in  their  prop- 
erties. There  is  a  practical  limit  to  this  subdivision, 
arising  from  the  imperfection  of  our  senses  or  our  tools, 
but  we  may  suppose  it  carried  on  till  the  very  smallest 
possible  fragments  remain  which  possess  the  properties  of 
the  substance. 

2.  Molecules. — To  these  fragments  we  give  the  name 
molecules.     They  are  definite  quantities  of  matter,  which 
have  size  and  weight. 

Hence  a  molecule  is  the  smallest  portion  of  any  substance 
in  which  its  properties  reside*  All  matter  is  made  up  of 
molecules.  We  know  that  molecules  must  be  extremely 
small.  Sixteen  ounces  of  gold,  which  in  the  form  of  a  cube 
would  not  measure  an  inch  and  a  quarter  on  a  side,  can  be 
spread  out  so  that  it  would  gild  silver  wire  sufficient  to 
reach  around  the  earth.  Its  thickness  must  then  be  at  least 

1  The  properties  of  matter  are  those  qualities  which  are  peculiar  to 
it, — which  belong  to  it  and  to  nothing  else. 

7 


8  NATURAL  PHILOSOPHY. 

one  molecule,  and  is  doubtless  many.  In  odors,  which 
produce  sensation  by  invisible  particles,  the  molecules 
scatter  about  through  the  atmosphere  for  years  without 
apparently  diminishing  the  size  of  the  substance  from 
which  they  are  separated.  Microscopists  have  found  ani- 
mals so  minute  that  four  million  of  them  would  not  be  so 
large  as  &  slti.glcr  gr£in  of  sand,  yet  each  has  its  organs  and 
its  circulating  fluids. ., 

3.  Siz£  of  a  Mpkenle.-—  The  methods  of  attaining  an  idea  of  the 
actual  dize  of  a  molecule  "are  too  abstruse  for  explanation  here,  but 
the  figures,  derived  from  experiments  of  different  kinds,  point  to 
UTo'.TJ'oir.irUTF  °f  an  inch  as  the  mean  diameter.     This  is  too  minute 
a  quantity  for  comprehension,  and  may  be  better  understood  by  the 
illustration  of  Sir  William  Thomson :    "If  we  conceive  a  sphere  of 
water  of  the  size  of  a  pea  to  be  magnified  to  the  size  of  the  earth, 
each  molecule  being  magnified  to  the  same  extent,  the  magnified 
structure  would  be  coarser-grained  than  a  heap  of  small  lead  shot, 
but  less  coarse-grained  than  a  heap  of  cricket-balls." 

The  molecules  of  hydrogen  gas  are  about  7,-jnri.TnnF  of  an  inch 
apart,  so  that  the  spaces  between  are  much  greater  than  the  molecules 
themselves. 

4.  Atoms. — When   the   division  is   carried   any  further 
than  molecules,  a  form  of  matter  with  new  properties  is 
produced.     It  is  not  possible  to  divide  a  molecule  by  me- 
chanical means,  but  heat  or  chemical  agents  can  separate 
it  into  two  or  more  portions.     Each  of  these  is  called  an 
atom.    An  atom  cannot  be  further  divided  by  any  means 
known  to  us. 

Hence  an  atom  is  the  smallest  possible  portion  of  matter. 

Experiment  i. — Put  a  piece  of  marble  or  chalk  (not  a  crayon) 
into  a  vessel,  and  pour  on  it  some  good  vinegar.  Bubbles  of  gas  will 
arise  through  the  water. 

A  molecule  of  marble  is  composed  of  a  number  of  atoms  of  dif- 
ferent substances.  The  acid  in  the  vinegar  causes  a  division  of  the 
molecule,  forming  new  substances.  One  of  these  substances  (carbonic 
acid)  is  a  gas,  which  passes  off  into  the  air.  The  others  remain  in 
the  vessel. 

5.  Constitution  of  Molecules. — The  molecules  of  some 


MATTER.  9 


substances  are  made  up  of  two  or  more  similar  atoms.  A 
molecule  of  hydrogen  gas  contains  two  atoms  exactly  alike. 
On  the  other  hand,  a  molecule  of  common  salt  contains  one 
atom  of  sodium  and  one  of  chlorine,  which  are  widely 
different  from  each  other  and  from  salt.  In  their  ordinary 
state,  sodium  is  a  soft  inflammable  solid,  and  chlorine  a 
greenish  gas.  A  molecule  of  sugar  is  composed  of  forty- 
five  atoms  of  three  different  kinds, — carbon,  which  we  can 
see  as  charcoal,  and  hydrogen  and  oxygen,  which  are  color- 
less invisible  gases. 

Experiment  2. — In  a  vessel  heat  a  small  portion  of  sugar  over  a 
fire.  A  black  substance  will  remain. 

In  this  case  heat  effected  a  separation  of  the  atoms  of 
the  molecules ;  the  gases  passed  off  into  the  air,  and  the 
solid  carbon  remained. 

6.  Elements. — If  the  molecules  of  a  substance  are  com- 
posed of  one  kind  of  atoms  only,  it  is  said  to  be  an  element. 
Sixty-five   elements  have  been  discovered  on  the  earth. 
Iron,  copper,  carbon,  are  elements.     "Water  and  air  are 
not. 

7.  Matter  Indestructible. — If  the  escaping  gases  and  the 
carbon  of  the  last  experiment  could  be  weighed,  the  sum  of 
the  weights  would  be  found  to  be  just  equal  to  the  weight 
of  the  original  sugar.     Hence  we  arrive  at  an  important 
property  of  matter, — it  is  indestructible. 

There  are  many  cases  of  the  apparent  destruction  of 
matter  in  combustion  and  chemical  action,  but  all  that  is 
done  is  to  change  its  form.  The  molecules  are  divided, 
and  the  atoms  form  new  combinations,  some  or  all  of  which 
are  invisible.  In  all  the  various  changes  continually  going 
on,  in  our  furnaces  and  laboratories,  and  in  nature,  not  a 
new  atom  is  ever  created.  According  to  the  best  of  our 
knowledge,  the  amount  of  matter  in  the  universe  has  re- 
mained unchanged  since  the  original  creation. 

8.  Matter  Porous. — The  molecules  of  matter  do  not  fit 


10  NATURAL  PHILOSOPHY. 

closely  together.  Hence  open  spaces,  or  pores,  are  left 
between  them.  We  then  arrive  at  a  property  of  matter 
which  is  believed  to  be  universal, — it  is  porous. 

Experiment  3. — Fill  a  tumbler  with  cotton-wool,  pressing  it  down 
so  firmly  that  the  vessel  will  hold  no  more.  Now  remove  the  cotton 
and  fill  the  vessel  with  alcohol.  With  care,  the  cotton  may  all  be 
replaced  without  spilling  the  alcohol.  The  cotton  has  gone  into  the 

?ores  of  the  alcohol,  and  the  alcohol  into  the  pores  of  the  cotton, 
t  is  impossible  to  conceive  that  the  molecules  of  both  substances 
occupy  the  same  space. 

9.  Matter  can  be  Expanded  and  Compressed. — As  a  result 
of  the  porosity  of  matter,  it  is  possible  to  expand  or  to  com- 
press it.     The  molecules  are  not  changed  in  form  or  size, 
but  they  are  further  separated  in  expansion,  and  crowded 
together  in  contraction,  so  that  the  substance  becomes  more 
porous  in  one  case  and  less  so  in  the  other.   Heat  in  general 
separates  the  molecules  from  one  another.     A  ball  that  will 
just  go  through  a  ring  when  cold  will  not  do  so  when  heated. 
The  mercury  in  a  thermometer-tube  rises  in  hot  weather 
because  the  heat  separates  the  molecules  and  there  is  no 
chance  for  expansion  in  any  other  direction.     The  ends 
of  the  rails  of  a  railroad-track  which  touch  each  other  in 
summer  are  separated  in  winter.     A  nail  can  be  driven 
into  wood  because  it  causes  a  compression  of  the  molecules 
around  to  make  a  place  for  it. 

Experiment  4. — On  a  cork 
floating  on  water  place  a  shav- 
ing. Set  it  on  fire,  and  put  over 
it  an  inverted  tumbler.  The  heat 
of  the  combustion  will  expand 
the  air  in  the  tumbler  and  force 
FIG.  l— EXPANSION  BY  HEAT.  it  out  under  the  edge  ;  what  is 

left  will  quickly  cool   and  con- 
tract, so  that  almost  immediately  the  water  will  rise  into  the  tumbler. 

10.  Expansion  by  Cold. — Heat  does  not  always  expand 
bodies. 

Experiment  5. — Fill  a  bottle  with  water,  and  cork  tightly.  Leave 
in  a  cold  place  till  the  water  is  frozen.  The  bottle  will  be  cracked. 

The  cold  here  caused  expansion.     At  39.2°  Fahrenheit  a 


MATTER. 


given  weight  of  pure  water  takes  up  least  room  and  ex- 
pands  with  a  change  of  temperature  either  way. 

11.  Some   Bodies  can  be  Hammered   into  Plates  and 
Drawn  into  Wires,— When  certain  solid  bodies  are  ham- 
mered out  into  plates  or  drawn  into  wires  the  molecules 
slide  past  one  another  and  arrange  themselves  differently. 
This  motion  of  the  molecules  is  not  possible  in  all  solid 
bodies,  and  some  possess  it  in  a  much  higher  degree  than 
others.     Gold  may  be  hammered  out  into  sheets  less  than 
•2"f)oYoo~o  °f  an  mc^  in  thickness.      Copper,  silver,  and  tin 
can  also  be  beaten  out  into  very  thin  foil.     One  of  the 
substances  which  may  most  readily  be  drawn  out  into 
wires  is  glass. 

Experiment  6. — Heat  in  an  alcohol  flame,  or  hot  gas  flame,  a  small 
glass  rod  or  tube.  When  red  and  soft,  it  may  be  drawn  out  into  a 
very  fine  thread. 

Metal  wire  is  made  by  drawing  the  soft  metal  through 
holes,  each  one  smaller  than  the  preceding.  Platinum  wire 
can  be  reduced  so  that  it  will  be  finer  than  the  finest  hair. 

12.  Matter  Elastic. — All  bodies  are  more  or  less  elastic. 
By  this  it  is  meant  that  when  compressed  within  certain 
limits  the  molecules  tend  to  come  back  to  their  original 
position  with  respect  to  one  another. 

When  a  ball  is  allowed  to  fall  on  a  hard  floor,  there  is  a 
compression  of  the  molecules  of  the  ball  near  the  point  of 
contact  with  the  floor.  The  elasticity  of  the  ball  causes 
an  immediate  restoration  to  the  original  form  of  the  ball, 
and  this  produces  the  rebound.  When  gases  are  com- 
pressed, they  recover  their  former  state  immediately  when 
the  pressure  is  withdrawn.  They  are  said  to  be  perfectly 
elastic.  Although  liquids  can  be  compressed  but  slightly, 
they  are  also  perfectly  elastic. 

13.  Tenacity. — When  the  molecules  of  a  solid  adhere 
so  closely  that   they  strongly  resist   a   force   tending  to 
pull  them  apart,  it  is  said  to  be  tenacious.     The  amount 
of  tenacity  depends   on   the   structure  of  the   substance. 


12  NATURAL  PHILOSOPHY. 

"Wrought  iron,  being  fibrous,  has  much  more  tenacity  than 
cast  iron,  which  is  granular.  Steel  is  very  tenacious.  A 
bundle  of  wires  will  support  much  more  weight  than  the 
same  material  in  solid  form.  Hence  the  cables  of  suspen- 
sion-bridges, which  have  to  hold  up  immense  weights,  are 
usually  made  up  of  bundles  of  fine  steel  wire. 

Experiment  7. — Place  a  piece  of  stick  on  two  supports  some  dis- 
tance apart,  and  break  it  by  a  weight  applied  in  the  middle.  Ex- 
amine the  fracture.  The  lower  fibres  will  be  found  to  be  separated. 

14.  Bridges. — When  a  weight  rests  on  a  bridge,  it  has  to  stand 
the  same  kind  of  strain  as  the  stick.     The  tendency  is  to  pull  it  apart 
at  the  bottom.     Hence  an  iron  bridge  has  its  lower  "  chord"  made  of 
tenacious  wrought  iron  rather  than  of  cast  iron.     The  upper  chord  is 
compressed,  and   as   cast   iron    will  stand  more   compression   than 
wrought  iron,  it  is  frequently  used  there. 

15.  Hardness. — Hardness  is   another  property  of  solid 
bodies,  depending  on  the  closeness  with  which  the  mole- 
cules stick  together  and  resist  the  entrance  of  another 
body  which  tends  to  penetrate  them.    Hard  bodies  are  not 
always  tenacious.     Diamond  is  the  hardest  of  substances, 
being  able  to   scratch   everything   else.     This,  ability  to 
scratch  is  the  test  of  hardness. 

Experiment  8. — Scratch  a  piece  of  glass  with  the  edge  of  a  quartz 
crystal  or  piece  of  flint.  Attempt  to  do  the  same  with  a  penknife- 
blade.  Quartz  is  harder  than  glass,  and  glass  is  harder  than  steel. 

16.  Density. — There  is  more  matter  in  the  same  space  in 
some  bodies  than  in  others.     This  is  either  because  the 
molecules  are  closer  together,  or  because  each   molecule 
contains  more  matter.     We  express   this  by  saying  that 
some  bodies  are  more  dense  than  others. 

17.  Volume. — The  volume  of  a  body  is  the  amount  of 
space  it  occupies. 

18.  Mass. — The  mass  of  a  body  is  the  quantity  of  mat- 
ter which  it  contains.     If  a  gas  be  heated  so  as  to  expand 
it,  the  mass  remains  the  same,  as  no  new  molecules  are 
formed,  but  the  density  decreases.     The  mass  therefore  de- 
pends on  two  things,  the  volume  and  the  density.     The 


MATTER.  13 


number  of  molecules  in  a  unit  (as  a  cubic  inch)  of  a  body 
multiplied  by  the  number  of  cubic  inches  gives  the  whole 
number  of  molecules.     In  other  words,  the  product  of  the 
volume  by  the  density  gives  the  mass,  or 
Mass  =  volume  X  density. 

19.  Unit  of  Length. — The  English  units  of  length  are 
the  inch,  the  foot,  and  the  yard ;  the  French  are  the  metre 
and  its  decimal  divisions.     It  is  convenient  to  remember 
that  a  metre  is  about  40  inches,  a  decimetre  about  4  inches, 
a  centimetre  about  -^  of  an  inch,  and  a  millimetre  -^  of  an 
inch.1 

20.  Unit  of  Surface. — For  square  measure  we  have  in 
English  the  square  inch,  square  foot,  and  square  yard,  and 
in  French  the  square  metre,  square  decimetre,  and  square 
centimetre.     The  cubic  units  are  derived  in  the  same  way. 

21.  Unit   of  Mass. — The  unit   of  mass  in  the  English 
system  is  the  pound  avoirdupois ;  in  the  French  it  is  the 
mass  of  a  cubic  centimetre  of  water  at  its  greatest  density, 
39.2°  F.     This  is  called  a  gram,  and  is  about  15 i  grains. 
This  is  divided  and  multiplied  decimally  for  smaller  and 
larger  weights. 

22.  Unit  of  Density. — The  unit  of  density  for  solids  and 
liquids  is  the  density  of  water  at  39.2°  F. 

23.  Affinity,    Cohesion,   Attraction.  —  The   force   which 
holds  together  the  atoms  in  a  molecule  is  called  affinity. 

The  force  which  holds  together  the  molecules  in  a  body 
is  called  cohesion. 

The  force  which  holds  together  the  different  bodies  of 
the  universe  is  called  attraction. 

Hence  affinity  makes  substances ;  cohesion  makes  bodies; 
attraction  makes  systems. 

Attraction  is  also  used  to  express  the  force  which  draws 
one  body  to  another,  as  in  the  case  of  magnets,  etc. 

1  The  metric  system  possesses  great  advantages,  especially  for  scien- 
tific people.  Appendix  I.  gives  it  in  part,  and  should  be  studied. 

2 


14  NATURAL   PHILOSOPHY. 

24.  Solids. — In  solid  bodies  the  molecules  preserve  their 
positions  with  considerable  firmness,  resisting  attempts  to 
displace  them.     Hence  these  retain  their  form  and  size. 
The  force  of  cohesion  in  them  is  strong. 

25.  Liquids. — In  liquid  bodies  there  is  perfect  freedom 
of  the  molecules  among  themselves,  so  that  the  bodies 
adapt  their  form  to  the  surrounding  vessel.     They  retain 
their  size,  but  change  their  form  with  the  slightest  force 
exerted  upon  them.     The  force  of  cohesion  in  them  is 
weak. 

26.  Gases. — In  gaseous  bodies  there  is  no  cohesion,  the 
molecules  have  a  repellent  action  upon  one  another,  so  that 
an  unrestrained  gas  will  expand  indefinitely. 

27.  Motion  of  Molecules. — The  molecules  of  all  bodies  are  be- 
lieved to  be  in  rapid  motion.     In  solids  this  is  restrained  by  cohesion, 
so  that  a  molecule  has  only  a  short  vibratory  motion.     In  liquids  the 
molecules  slide  over  one  another  without  resistance,  restrained  only 
when  they  reach  the  sides  of  the  enclosing  vessel.     This  contact  pro- 
duces the  pressure  against  the  sides.      In  gases  the  molecules  are 
strongly  repelled  from  one  another,  and  dash  about  with  great  ve- 
locity.    Hence  there  are  constant  collisions   among  them  and  with 
other  bodies.     Our  bodies  are  subject  to  this  incessant  battering  by 
the  little  molecules  of  the  atmosphere,  but,  the  force  being  the  same 
on  both  sides  of  the  tissues,  we  do  not  notice  it. 

28.  Adhesion. — Adhesion  differs   from  cohesion  in  that 
it  acts  between  molecules  of  different  bodies.     The  force 
which  causes  mortar  to  stick  to  bricks,  which  causes  a 
pencil  to  leave  a  mark  on  paper,  which  enables  glues  and 
pastes  to  be  effective,  is  adhesion.     It  is  also  something 
like  adhesion  which  causes  water  to  rise  in  a  small  tube 
or  on  the  side  of  a  glass  plate. 

29.  Weight. — The  weight  of  bodies  results  from  attrac- 
tion.    All  bodies  attract  all  other  bodies.     The  more  mole- 
cules a  body  contains,  the  greater  is  its  attraction  for  others, 
and  the  attraction  of  others  for  it.     The  pull  of  all  the  par- 
ticles of  the  earth  on  the  objects  on  its  surface  is  the  same 
as  if  one  strong  pull  drew  them  to  its  centre.     Hence  a 


MATTER.  15 


plumb-line  points  to  the  centre  of  the  earth,1  and  different 
plumb-lines  are  not  parallel,  but  converge  downward. 

30.  Gravity,  —  The    attraction   of   the   earth   is    called 
gravity. 

31.  Weight  Proportional  to  Mass.— The  earth  pulls  every 
particle  of  a  body.     If  we  suppose  a  string   attached  to 
each  molecule,  and  all  the  strings  pulled  by  equal  forces, 
we  would  have  the  case  of  attraction.     Hence  the  more 
molecules  the   greater  the  attraction.     But  the  mass  is 
determined  by  the  number  of  molecules.     Hence  we  have 
the  law, — 

Under  the  same  conditions  the  weights  of  bodies  (or  the 
total  attractions)  are  proportioned  to  their  masses. 

32.  Weight  Inversely  Proportional  to  Square  of  Distance. 
— The  position  of  the  body  affects  the  weight.     The  attrac- 
tion diminishes  as  the  bodies  recede  from  each  other.     If 
the  distance  doubles,  the  attraction  is  only  one-fourth,  and 
if  the  distance  trebles,  one-ninth,  of  the  original  amount. 
We  express  this  by  saying,  The  attraction  varies  inversely  as 
the  square  of  the  distance. 

33.  Mass  Constant. — The  position  of  the  body  does  not 
affect  the  mass.     It  might  be  removed  far  from  the  earth 
and  the  mass  would  be  the  same.     The  number  of  mole- 
cules— i.e.,  the  mass — would  be  constant  if  carried  to  the 
sun ;  but  as  there  is  so  much  more  mass  in  the  sun  than 
in  the  earth,  the  attraction,  and  consequently  the  weight 
of  the  body,  would  be  greatly  increased. 

34.  Unit  of  Weight. — The  unit  of  weight  is  the  same  as 
the  unit  of  mass,  the  gram. 

35.  Mobility  and  Inertia. — Bodies  will  not  move  unless 
some  force  is  exerted  on  them  from  without,  and  they  yield 
to   the   slightest   force   impressed  which   is   not   counter- 
balanced by  some  other  force.     This  brings  us  to  two  other 

1  This  is  very  slightly  modified  by  the  fact  that  the  earth  is  not  a 
perfect  sphere. 


16  NATURAL  PHILOSOPHY. 

properties  of  matter, — mobility,  which  induces  it  to  yield 
freely  to  impressed  forces,  and  inertia,  which  prevents  it 
from  moving  itself,  or  from  changing  any  motion  which 
may  be  given  it.  Matter  has  no  power  to  move  or  to  resist 
an  unbalanced  force. 

Examples  of  inertia  are  numerous.  It  requires  more 
force  to  start  a  car  than  to  keep  it  in  motion.  When  sud- 
denly stopped  by  another  force,  the  contents  are  thrown 
forward  by  their  inertia.  A  ball  projected  upward  stops, 
not  because  it  has  power  to  stop  itself,  but  because  another 
force,  gravity,  is  constantly  pulling  against  its  motion.  A 
marble  thrown  swiftly  through  a  pane  of  glass  will  make 
a  small  round  hole,  because  the  inertia  of  the  other  parts 
of  the  glass  prevents  them  from  yielding  to  the  sudden 
impression. 

Experiment  9. — Place  a  card  on  the  end  of  a  finger,  and  a  cent  on 
the  card.  By  a  quick  stroke  with  the  forefinger  of  the  other  hand 
the  card  may  be  shot  out,  leaving  the  cent  resting  on  the  finger. 

36.  Ether. — We   have   spoken    of   the   three    forms   of 
matter,  solid,  liquid,  and  gaseous ;  we  have  also  said  that 
the  molecules  of  matter  do  not  fill  up  the  whole  space,  but 
that  pores,  which  are  large  compared  with  the  size  of  the 
molecules  themselves,  exist  in  all  substances.     This  inter- 
molecular  space  is  supposed  to  be  filled  with  something 
called  ether,  which  is  as  far  separated  from  gases  by  its 
properties  as  gases  are  from  liquids.     It  also  fills  the  pores 
of  the  air,  and  the  spaces  between  the  planets  and  between 
the  stars,  outside  the  bounds  of  the  atmospheres  which 
surround  them.      It  is    highly  elastic,  without  weight  or 
color,  or  any  other  properties  which  can  be  perceived  by 
the  senses.     It  is  supposed  to  be  the  agent  which  by  its 
vibratory  motion  conveys  the  rays  of  light  from  the  sun 
to  the  earth,  and  which  carries  them  between  the  molecules 
through  transparent  substances. 

37.  Radiant  Matter. — Dr.  William  Crookes1  has  found 

1  An  English  scientist,  now  living  (1883). 


MATTER.  17 


that  by  exhausting  the  air  in  a  tube  so  as  to  leave  not  more 
than  one-millionth  the  ordinary  amount,  the  remaining  sub- 
stance has  such  peculiar  properties  that  he  feels  justified 
in  giving  it  a  new  name.  He  calls  it  radiant  matter,  and 
considers  it  to  be  the  fourth  form.  Solid,  liquid,  gaseous, 
and  radiant  would  then  be  the  four  aggregate  states,  each 
having  properties  which  widely  separate  it  from  the  others. 
By  passing  electric  sparks  through  radiant  matter  some  of 
its  properties  have  been  determined.1  Of  the  properties 
of  ether  we  know  nothing  by  direct  experiment,  but  it  is 
considered  likely  that  it  is  a  form  of  radiant  matter. 

38.  Summary. — Matter  is  made  up  of  a  countless  number 
of  minute  molecules.     It  is  perfectly  inert,  but  each  par- 
ticle possesses  the    property   of   attracting   every   other 
particle.     It  has  extension  in   three    directions,  and  has 
three  (probably  four)  forms  of  aggregation. 

39.  Natural  Philosophy. — Natural  Philosophy  treats  of 
the  laws  of  cohesion,  the  molecular  properties  of  matter, 
and  the  effects  of  the  action  of  forces  upon  matter. 

40.  Astronomy. — Astronomy  treats   of  matter  in  large 
masses,  and  of  the  laws  of  gravitation. 

41.  Chemistry. — Chemistry  treats  of  the  atomic  proper- 
ties of  matter,  and  of  the  laws  of  affinity. 

Exercises. — 1.  Is  matter  destroyed  when  water  is  dried  up?  when 
gunpowder  explodes  ?  when  house  gas  burns  ?     Where  does  it  go  to? 

2.  To  what  property  of  matter  do  blotting-pads  owe  their  utility  ? 
rubber  bands  ?  watch-springs  ?  pop-guns  ?  putty  ?  hammers  ?  piano- 
strings  ?  water-filters  ? 

3.  Why  does  not  the  addition  of  a  little  sugar  to  a  full  cup  of 
coffee  cause  it  to  overflow  ? 

4.  When  we  fix  the  head  of  a  hammer  on  the  handle  by  striking 
the  end  of  the  handle  on  a  block,  what  property  do  we  use? 

5.  Why  does  a  foot-ball,  nearly  empty,  become  full  when  we  ex- 
haust the  air  from  around  it  ?  why  does  it  soon  collapse  ? 

6.  One  sixteen-thousandth  of  a  cubic  inch  of  indigo  dissolved  in 
sulphuric  acid  can  color  two  gallons  of  water.     What  property  of 
matter  is  here  shown  ? 

7.  How  would  you  test  the  relative  hardness  of  two  minerals  ? 

1  These  will  be  further  explained,  page  314. 
b  2* 


18  NATURAL   PHILOSOPHY. 


8.  When  water  is  converted  into  steam,  are  the  molecules  enlarged 
or  separated?  is  its  mass  increased  or  diminished?  its  density?  its 
weight  ?  its  volume  ? 

9.  Name  a  substance  which  is  often  found  in  all  three  forms. 

10.  If  you  knew  the  volume  and  mass  of  a  solid,  how  would  you 
obtain  its  density  ?  if  you  knew  its  mass  and  density,  how  would  you 
obtain  its  volume? 

11.  Give  an  instance  of  a  hard  body  which  has  little  cohesion. 

12.  Why  does  not  a  large  stone  fall  to  the  earth  more  rapidly  than 
a  small  one  ? 

13.  If  a  body  were  removed  to  a  distance  of  8000  miles  from  the 
surface  of  the  earth,  how  much  less  would  it  weigh  than  at  the  sur- 
face?    Ans.  ^  as  much. 

14.  What  would  a  100-pound  weight  weigh  if  moved  to  the  dis- 
tance of  the  moon  (60  radii  of  the  earth)  ?     Ans.  ^  pound. 

15.  Suppose  a  sphere  were  one-half  the  diameter  of  the  earth  and 
of  the  same  density,  what  would  a  body  which  weighed  100  pounds 
on  the  earth  weigh  at  its  surface?     Ans.  50  pounds. 

Note. — Its  mass  would  be  one-eighth  that  of  the  earth,  and  dis- 
tance of  the  body  from  its  centre  one-half. 


MOTION  AND  FORCE. 


19 


CHAPTER    II. 
MOTION  AND   FORCE. 

42.  Rest  and  Motion. — A  body  is  at  rest  when  it  does  not 
change  its  place.     It  is  in  motion  when  it  does  change  its 
place. 

No  body  with  which  we  are  acquainted  is  at  rest.  The 
earth  and  all  that  is  on  it  move  with  great  velocity.  The 
sun  moves,  and  so  do  the  stars.  But  when  a  book  lies  on  the 
table  it  does  not  move  with  respect  to  the  surrounding  bodies 
or  the  earth.  It  is  at  relative  rest,  but  in  absolute  motion. 

43.  Kinds  of  Motion. — When  a  body  in  motion  passes 
over  equal  spaces  in  equal  times,  its  motion  is  uniform. 
When  it  passes  over  unequal  spaces  in  equal  times,  its 
motion  is  varied.     When  the  spaces   in  successive  times 
become  greater,  its  motion  is  accelerated,  and  when  less,  re- 
tarded.    This  acceleration  or  retardation  may  also  be  uni- 
form or  varied. 

44.  Velocity. — The  velocity  of  a   motion   is   the   space 
traversed  in  the  unit  of  time.     It  may  be  in  miles  per 
hour,  feet  per  second,  etc. 


Feet  moved  in  Successive  Seconds. 

Kinds  of  Motion. 

30 

30 

30 

30 

Uniform. 

10 

15 

20 

25 

Uniformly  accelerated. 

20 

18 

16 

14 

Uniformly  retarded. 

20 

14 

16 

4 

Varied,  —  not  uniformly. 

Questions. — When  a  train  starts  from  a  station,  what  kind  of 
motion  is  it  ?  when  stopping  ?  when  a  ball  is  thrown  upward  ?  when 
it  falls  ?  What  kind  of  motion  in  the  hands  of  a  watch  ?  in  the  cur- 
rent of  a  river  ?  in  the  winds  ? 

45.  Force. — Force  is  anything  which  tends  to  produce,  change, 


20  NATURAL   PHILOSOPHY. 

or  destroy  motion.  If  it  acts  on  a  body  at  rest,  it  produces 
motion.  If  it  acts  on  a  body  in  motion,  it  may  change  the 
direction  or  velocity  of  the  motion,  or  destroy  it.  Two  or 
more  forces  may  act  on  a  body  at  rest  so  as  to  balance  each 
other  and  cause  no  motion.  But  each  one  tends  to  produce 
motion.  In  bridges  and  buildings  we  have  cases  of  bal- 
anced forces.  Gravity  is  a  force  always  acting  upon  them, 
and  upon  everything  they  sustain.  This  produces  other 
forces  acting  along  the  various  timbers  and  pieces.  If  the 
structure  is  well  built,  the  strains  from  these  forces  are 
exactly  balanced,  every  part  is  sufficiently  strong  to  do  its 
work,  and  there  is  no  motion  except  such  as  is  due  to  the 
elasticity  of  the  materials. 

46.  Kinds  of  Force.— A  force  may  act  for  an  instant  and 
then  cease,  in  which  case  it  is  said  to  be  an  impulsive  force ; 
or  it  may  act  for  some  time,  when  it  is  a  continuous  force. 
The  striking  of  a  ball  by  a  bat  is  an  example  of  an  impul- 
srve  force,  and  the  pulling  of  a  train  by  a  locomotive,  of  a 
continuous  force. 

47.  Impulsive  Force  produces  Uniform  Motion. — An  im- 
pulsive force  tends  to  produce  uniform  motion,  and  a  continuous 
force  accelerated  motion.    This  would  seem  to  be  contradicted 
by  experience.     For  the  motion  of  a  ball  is  soon  destroyed, 
and  the,  continual  pull  of  the  engine  may  only  keep  the 
train   moving   uniformly.      But   the   force  of  the  bat  or 
of  the  locomotive  does  not  act  alone.     Were  it  not  for 
gravity,  the  resistance  of  the  air,  and  friction,  which  are 
modifying  forces,  the  ball  would  move  on  forever  with 
uniform  velocity,  and  the  velocity  of  the  train  would  be 
accelerated  so  long  as  the  engine  pulled  it  ever  so  slightly. 

48.  Newton's  Laws  of  Motion. — All  the  circumstances 
of  motion  are  embraced  in  three  laws,  first  enunciated  by 
Sir  Isaac  Newton.     These  cannot   be  proved  mathemati- 
cally.    They  should  be  looked  upon  as  fundamental  prin- 
ciples, which  depend  on  the  properties  of  matter,  and  which 
may  be  shown  to  be  true  by  experiment. 


MOTION  AND   FORCE.  21 

1.  A  body  at  rest  remains  at  rest,  and  a  body  in  motion  con- 
tinues to  move  forward  in  a  straight  line,  until  acted  on  by 
force  external  to  it. 

2.  Motion  or  change  of  motion  is  proportional  to  the  force 
impressed,  and  is  in  the  straight  line  in  which  the  force  acts. 

3.  When  bodies  act  on  each  other,  action  and  reaction  are 
equal  and  in  opposite  directions. 

The  first  law  is  the  result  of  the  inertia  of  matter,  and 
the  second,  of  its  mobility.  The  first  says  matter  can  do 
nothing  itself,  and  the  second,  that  the  slightest  force  will 
have  its  corresponding  effect. 

The  third  law  may  be  made  clear  by  some  illustrations. 
The  earth  attracts  an  apple  and  causes  it  to  fall.  The 
apple  attracts  the  earth  just  as  strongly,  and  the  earth 
moves  to  meet  it,  but  the  greater  mass  of  the  earth  makes 
it  move  so  little  that  the  motion  is  not  noticed.  When  you 
hold  up  a  body  in  your  hand,  the  hand  presses  up  just  as 
hard  as  the  body  presses  down.  The  reaction  of  the  wfcjer 
on  the  oar,  and  on  the  fins  of  a  fish,  causes  the  boat  or  the 
fish  to  advance ;  the  reaction  of  the  air  on  the  wings  causes 
the  bird  to  sustain  itself  and  to  move  forward. 

49.  Momentum. — Momentum  is  the  quantity  of  motion.  The 
momentum  of  the  earth  was   the  same  as  the  momentum 
of  the  apple.     For  while  its  velocity  was  less,  its  mass  was 
as  many  times  greater.     Hence  mass  and  velocity  together 
make  up  momentum.     A  body  weighing  two  pounds  has 
twice  the  motion  of  one  of  one  pound  which  has  the  same 
velocity ;  a  body  with  twice  the  velocity  of  another  has 
twice  the  motion,  the  mass  being  the  same.    In  general  we 
have  the  equation, — 

Momentum  =  mass  X  velocity. 

50.  Measure  of  Forces. — We  may  measure  forces  in  two 
ways.     One  way  is   by  the  pressure  necessary  to  resist 
them, — weighing  the  forces,  as  it  were.     The  unit  would 
then  be  in  the  English  system  the  pound,  and  in  the  French 
system  the  gram.     These  would  vary  as  gravity  varied, 


22 


NATURAL   PHILOSOPHY. 


being  greater  nearer  the  level  of  the  sea.  A  better  way 
to  measure  forces  is  by  the  velocity  they  would  produce. 
We  have  here  also  two  systems. 

In  the  English,  the  unit  of  force  is  the  force  which,  acting 
for  one  second,  will  cause  a  pound  of  matter  to  have  a 
velocity  of  a  foot  a  second. 

In  the  French,  it  is  the  force  which,  acting  for  one  second, 
will  cause  a  gram  of  matter  to  have  a  velocity  of  a  centi- 
metre a  second.  This  unit  is  called  the  dyne  (pronounced 
dine),  and  is  coming  into  general  use  among  scientific  men. 

51.  Acceleration. — The  velocity  which  a  force  would 
produce  in  a  unit  of  mass  in  a  second  is 
called  its  acceleration. 

52.  Illustrations. — We   will  now  illus- 
trate some  of  these  terms.      If  a   body 
weighing  20  grams  has  a  velocity  of  10 
centimetres  a  second,  its    momentum  is 
200.     (This  is  not  foot-pounds  or  grams 
or  centimetres;  the  unit  of  momentum 
has  no  name.) 

If  this  momentum  is  produced  by  a 
force  acting  for  1  second,  it  is  a  force 
of  200  dynes;  if  for  5  seconds,  it  is  a 
force  of  40  dynes. 

53.  Acceleration  a  Measure  of  Force. — 
If   a   force   acting   on   the   body   for   1 
second  will  give  it  a  velocity  of  10  cen- 
timetres, the  acceleration  is  10.     During 
every  succeeding  second  which  it  acts,  it 
adds  10  centimetres  to  its  velocity.     As 
its  inertia  keeps  the  body  moving  at  its 

former  velocity,  this  continual  force  constantly  increases 
its  velocity.  The  greater  the  force,  the  greater  will  be 
the  velocity  produced  the  first  second.  The  acceleration  is 
a  measure  of  the  force. 

54.  Dynamometer. — A  practical  way  of  measuring  some 


FIG.  2. — DYNAMOMETER. 


MOTION  AND  FORCE.  23 

forces  is  by  a  spring-balance  placed  in  the  line  through 
which  the  force  must  act.  A  dynamometer  (Fig.  2)  is  an 
instrument  of  the  same  kind,  registering  the  amount  of 
force  expended.  It  is  used  to  determine  the  resistance  to 
motion  of  a  train,  wagon,  plough,  or  other  instrument. 

If  a  body  be  hung  on  a  spring-balance,  we  weigh  the 
force  of 'gravity.  If  a  spring-balance  or  dynamometer  is 
placed  between  a  horse  and  a  plough,  we  weigh  in  the 
same  manner  the  force  of  the  pull  of  the  horse.  If  the 
horse  pulls  with  a  force  of  200  pounds,  this  means  that  the 
connection  with  the  plough  is  strained  just  as  a  rope  would 
be  if  sustaining  a  weight  of  200  pounds. 

Questions. — 1.  What  kind  of  force  is  gravity?  what  kind  of 
force  drives  the  bullet  from  the  gun  ?  what  kinds  of  motion  would 
they  produce  if  unmodified  ? 

2.  Which  of  Newton's  laws  are  illustrated  by  the  breaking  of  an 
egg  against  a  table  ?  by  the  tendency  of  a  train  to  be  thrown  out- 
ward over  a  curve  ?  in  the  throwing  of  a  ball  ?  in  the  fact  that  it  is 
more  difficult  to  start  a  train  than  to  keep  it  in  motion  ? 

3.  A  body  weighing  20  pounds  has  a  momentum  of  400:  what  is 
its  velocity  in  feet  per  second  ? 

4.  Two  bodies,  one  of  20  and  one  of  2  pounds,  are  drawn  together 
by  their  mutual  attractions :  which  will  move  the  faster,  and  how 
much  ? 

5.  A  body  of  20  grams  and  a  velocity  of  10  centimetres  per  second 
meets  another   body  of  40  grams  moving  in  the  opposite  direction 
with  a  velocity  of  4  centimetres  per  second :  in  what  direction  will 
the  bodies  move  after  impact  ?    Ans.  In  the  direction  of  the  first. 

6.  How  many  dynes  of  force  are  required  to  produce  a  velocity  of 
500  centimetres   per  second  in  a  body  of  200  grams  weight  in  5 
seconds?    Ans.  20,000. 

7.  What  would  be  the  mass  if  20  dynes  of  force  would  produce  in 
5  seconds  a  velocity  of  5  centimetres  per  second  ?    Ans.  20. 

8.  In  how  many  seconds  would  a  force  of  40  dynes  produce  a 
momentum  of  400  units  ?     Ans.  10. 

55.  Representation  of  Forces. — A  force  may  be  repre- 
sented by  a  straight  b 

line.     Thus,  the  line  ab 

indicates  that  the  force  acts  on  a  body  at  a  in  the  direction 
ab.  The  length  of  the  line  may  also  represent  the  mag- 
nitude of  the  force.  A  line  twice  as  long  would  represent 
twice  as  great  a  force. 


24  NATURAL   PHILOSOPHY. 

56.  Resultant. — The  resultant  of  two  or  more  forces  is 
the  name  given  to  a  single  force  which  would  produce  the 
same  effects. 

If  two  forces,  one  of  2  pounds  and  one  of  4,  act  on  a 


FIG.  3.—  FORCES  IN  A  LINE. 

body  at  a  in  the  same  direction,  their  resultant  is  evidently 
a  force  of  6  pounds  acting  in  the  same  direction.  If  they 
act  in  opposite  directions,  their  resultant  is  the  difference 
of  their  forces  (2  pounds),  and  acts  in  the  direction  of  the 
greater.  !By  considering  one  direction  as  positive  and  the 
other  as  negative,  we  express  both  of  these  cases  by  a 
single  law. 

57.  Resultant  of  Parallel  Forces.  —  The  resultant  of  two 
or  more  parallel  forces  is  their  algebraic  sum. 

If  in  one  direction  we  have  forces  of  6,  2,  4,  and  in  the 
other  3,  7,  1,  the  resultant  is  6  -f  2  -f  4  —  3  —  7  —  1  =  4-1. 
The  resultant  is  1,  and  acts  in  the  direction  of  the  plus 
forces. 

58.  Parallelogram  of  Forces.  —  If  the  forces  do  not  act 

in  the  same  line,  they  may  still 
-have  a  single  resultant. 

Let  the  forces  p  and  q  act  on 
a  at  the  same  time  in  the  direc- 
tions given  in  the  figure.  Ac- 
cording  to  Newton's  second  law, 

°f  the 


FIG.  ^.-PARALLELOGRAM  OF  FORCES. 

full   effect  on   the   body.      The 

force  p  would  carry  it  somewhere  in  the  line  ab,  but  the 
force  q  is  such  as  to  take  it  over  the  space  ac.  Hence  it 
would  bring  it  into  the  line  cd,  parallel  to  ab.  By  the  same 
reasoning  the  body  would  be  shown  to  be  brought  into  the 
line  bd,  parallel  to  ac.  If  it  is  brought  into  both  of  these 


MOTION  AND   FORCE.  25 


lines  it  must  be  brought  to  their  place  of  meeting  at  d. 
The  figure  abdc  is  a  parallelogram,  and  is  called  in  this 
case  the  parallelogram  of  forces.  The  body  would  move  in 
a  straight  line,  ad,  which  is  the  diagonal  of  the  parallelo- 
gram, and  its  motion  would  be  the  same  as  if  acted  on  by 
the  single  force  r.  Hence  r  is  the  resultant  of  p  and  q. 

59.  Triangle  of  Forces.  —  If  we  consider  the  forces  with- 
out reference  to  their  point  of  application,  ab,  bd,  and  ad 
will  represent  them,  and  will  form  a  triangle.     A  force  act- 
ing at  a,  equal  and  opposite  to  ad,  will  balance  ad.    Hence 
the  three  forces  ab,  bd,  and  da  (notice  the  order  of  the 
letters)  will  form  a  system  which  is   balanced.     We  have 
a  general  truth  that  if  three  forces  are  represented  in  mag- 
nitude and  direction  by  the  sides  of  a  triangle  taken  in 
order,  the  system  is  balanced. 

60.  Resultant  of  any  Number  of  Forces.  —  If  more  than 
two  forces  act  on  one  point,  we  must  find  the  resultant  of 
two  of  them  ;  then  of  this  resultant  and  a  third  force  ;  and 
so  on. 

If  ab,  ac,  ad,  and  ae  are  forces  acting  at  a,  then  the  re- 
sultant of  ab  and  ac  is  ar  ;  of  ar  and 
ad,  ar'  ;  and  of  ar'  and  ae,  ar".     It 
will  be   observed  that  abrr'r"  is 
polygon,  four  of  the  sides  of  which 
are  parallel  to  the  forces,  and  the 
fifth  represents  the  resultant.  ---    dT 

61.  Polygon  of  Forces.  —  This  prin- 

.    -i  i  ,     ,    ,  ,  7  FIG.  5.  —  POLYGON  OF  FORCES. 

ciple  is  called  the  polygon  of  forces, 

and  may  be  stated  as  follows  :  If  a  figure  be  constructed 

having  the  sides  equal  and  parallel  to  the  forces,  the  line 

necessary  to  close  this  polygon,  drawn  from  the  starting- 

point,  will  represent  the  magnitude  and  direction  of  the 

resultant. 

Also,  if  the  forces  acting  on  a  body  be  represented  in 
magnitude  and  direction  by  the  sides  of  a  polygon  taken 
in  order,  the  system  is  balanced. 
B  3 


It       i 
a 

h  - 


26 


NATURAL   PHILOSOPHY. 


62.  Forces  not  in  a  Plane. — If  the  forces  are  not  all  in 
one  plane,  the  method  would  produce  the  outlines  of  a 
solid  body. 

If  ab,  ac,  ad  be  three  forces  not  in  one  plane,  ar  is  the 
resultant  of  the  first  two,  and  ar'  the  final  resultant.1 


b 

FIQ.  6.— PARALLELOPIPED  OF  FORCES. 


Fio.  7. — RESOLUTION  OP  FORCES. 


63.  Composition  and  Resolution.  —  The  force  ar  may  be 
divided  into  two  forces,  ab  and  ac,  or  into  ae  and  of,  or,  in 
general,  into  any  two  which  with  it  would  make  a  triangle. 

Combining  forces  so  as  to  get  a  resultant  is  called  the 
composition  of  forces,  and  separating  single  forces  into  sev- 
eral parts  is  called  the  resolution  of  forces.  The  parts  are 
called  components. 

Experiment  10.  —  Fasten  two  pulleys  against  a  vertical  board  so 

that  they  will  turn  freely.  Arrange 
cords  as  in  the  figure,  making  the 
knot  at  a  so  as  not  to  slip.  Hang 
weights  p,  <7,  and  r,  being  careful  not 
to  get  r  greater  than  p  and  q  com- 
bined. Measure  off  ab  and  ac  pro- 
portional to  the  weights  p  and  q,  and 
draw  lines  on  the  board  to  complete 
the  parallelogram  abdc.  Measure  ad, 
and  it  will  be  found  to  be  equal  to  r 
on  the  same  scale  that  ab  and  ac  were 
made  ;  also  the  point  d  will  be  found  to  be  directly  over  a. 

This  shows  that  the  diagonal  ad  represents  the  resultant 
in  magnitude  and  direction. 


FIG.  8.—  RESOLUTION  OF  FORCES. 


1  If  the  forces  do  not  all  act  on  the  same  point  in  the  body  the 
problem  becomes  too  complex  for  this  treatise. 


MOTION  AND   FORCE. 


27 


between  a 


FIG.  9.— CROSSING  A  CURRENT. 


Experiment  n. — Place  spring  balances  in  the  strings 
and  the  pulleys,  and  measure  the  forces  in  this  way. 

64.  Rowing  across  a  Current. — If  a  man  undertakes  to 
row  straight  across  a  river  6        f 

in  which  there  is  a  current, 
his  course  will  be  oblique. 
For  let  ab  represent  the 
force  of  his  rowing,  and  ac 
the  force  of  the  current. 
Then  the  resultant  ad  will  be  the  direction  of  his  course, 
and  he  will  land  at  /  instead  of  at  e.  If  he  wants  to  go 
straight  across,  he  will  steer  in  the  direction  a'b',  so  that 
a'b'  combined  with  a'c'  will  have  a  resultant  in  the  direc- 
tion a'e'. 

65.  Sailing  a  Boat. — In  sailing  a  boat  we  have  a  good 
illustration  of  the  resolution  of  forces.    Let 

ab  be  the  keel,  cd  the  direction  of  the  sail, 

and  fe  the  force  of  the  wind,    fe  may  be 

resolved  into  two  forces,  fg,  parallel  to  the 

sail,  which  would  have  no  effect  in  driving 

the  vessel  forward,  and  ge,  perpendicular 

to  it.     The  force  ge  may  again  be  resolved 

into  gh,  perpendicular  to  the  keel,  and  he, 

in  its  direction.     This  latter  force  is  all  that  is  effective  in 

propelling  the  boat.     The  force  gh  tends  to  upset  it.     In  a 

complete  analysis  of  forces  the  action  of  the  rudder  must 

also  be  taken  into  account. 

66.  Component  Forces  greater  than  the  Original. — It  is 
possible  to  resolve  a  force  into  two  components  each  of 
which  shall  be  much  greater  than  the  original  force.     If  in 
Fig.  8  the  weight  r  should  be  very  small,  the  line  between 
the  pulleys  would  be  nearly  straight,  and  by  constructing 
the  parallelogram  it  would  be  seen  that  the  components 
along  ab  and  ac  would  be  much  greater  than  r.     The  same 
principle  is  shown  in  the  knee-joint  (Fig.  11).   This  consists 
of  a  pair  of  levers,  jointed  together  at  b.     One  of  them  is 


Fia.  10.— SAILING  A 
BOAT. 


28  NATURAL  PHILOSOPHY. 

firmly  fixed  at  the  end  a,  the  other  is  attached  to  a  movable 
6  slide.     Any  force,  p,  acting  verti- 

cally on  the  joint  will  be  resolved 
into  two,  one  along  each  lever. 
The   more   obtuse   the   angle  at 
FIG.  H.-KNEE-JOINT.  the  joint,  the  greater  will  be  the 

component    forces   as    compared 
with  the  applied  force. 

Experiment  12. — Stretch  a  string  tightly  between  two  fastenings. 
Tie  a  weaker  string  to  its  middle  point.  By  pulling  this  the  stronger 
string  breaks  first  For  the  component  pull  is  stronger  than  the 
original. 

67.  Centrifugal  Force. — When  a  body  is  swung  around 

by  a  string  there  are  two  forces  acting 
on  it.     One   is  its   inertia,  which  would 
tend  to  cause  it  to  move  in  a  line,  ab, 
touching  the  curve.     The  other  is  #c,  the 
pull  of  the  string.     The  tendency  would 
be  to  move  in  the  diagonal  ad.    But  as  this 
pull  is  acting  continuously,  and  the  direc- 
tion continually  changing,  the  line  is  a 
Fw' 12< "C™VEION  IN  A     curve-     These  are  the  forces  which  keep 
the  earth  and  all  the  planets  in  their  orbits. 
The  outward  pull  on  a  string,  which  is  the  result  of  the 
inertia  of  the  body  tending  to  cause  it  to  get  farther  from 
the  centre,  is  centrifugal  force.     It  is  always  opposite  and 
equal  to  the  force  drawing  towards  the  centre. 

68.  Centrifugal  Force  Apparatus. — Its  effect  is  shown  in 
the  centrifugal  force  apparatus  of  Fig.  13.    Here  the  flexible 
bands  are  put  in  rapid  rotation,  and  the  centrifugal  force 
makes  them  assume  the  form  indicated  by  the  dotted  line. 

69.  Effects  of  Centrifugal  Force. — There  are  many  other 
illustrations  of  centrifugal  force.     When  the  earth  was  a 
soft  body,  the  centrifugal  force  caused  by  its  rotation  on  its 
axis  probably  produced  the  bulging  at  the  equator  which  we 
now  notice.    The  centrifugal  force  is  greater  at  the  equator 


MOTION  AND  FORCE. 


29 


than  elsewhere,  because  of  the  greater  velocity  of  the  earth 
there.  Hence  bodies  are  lighter  there  than  at  the  poles. 
An  equestrian  leans  inward  in  riding  around  a  curve,  to 


FIG.  13. — CENTRIFUGAL  FORCE  APPARATUS. 

balance  the  centrifugal  force.    It  is  this  force  which  causes 
mud  to  fly  off  moving  carriage-wheels,  or  water  from  a 
grindstone,  and  which  sometimes  breaks  a  rapidly-revolv- 
ing fly-wheel.     In  sugar-refineries 
the  syrup  is   separated   from   the 
crystals  by  being  thrown  outward, 
the  sugar  being  retained  by  a  wire 
gauze.    Clothes  are  dried  by  a  simi- 
lar arrangement.     In  a  bicycle  in 
motion  the  centrifugal  force  causes 

the  particles  to  continue  to  move  in  the  same  plane.   Hence 
the  faster  it  is  going  the  more  difficult  it  is  to  overturn. 

70.  Moment  of  a  Force. — The  moment  of  a  force  is  its 
ability  to  produce  rotation.  If  be  be  a  lever  attached  to  a 
body  which  has  power  to  rotate  about  an  axis  at  a,  and  a 

3* 


FIG.  14.— MOMENT  OF  A  FORCE. 


30  NATURAL   PHILOSOPHY. 


force  be  applied  at  b,  in  the  direction  of  the  arrow-head,  it 
will  tend  to  produce  rotation.  This  ability  will  depend  on 
the  magnitude  of  the  force  and  the  length  of  its  lever- 
arm,  and  is  equal  to  their  product.  Thus,  the  moment  of 
p=pX  ab. 

1.  A  force  of  10  pounds  has  a  lever-arm  of  2  feet:  what  is  its 
moment? 

Ans. — 20  foot-pounds. 

2.  A  force  of  16  grams  has  a  lever-arm  of  200  metres :  what  is  its 
moment  in  kilogram-metres  ? 

If  a  man  attempt  to  overturn  a  heavy  pillar,  he  will  push 
against  it  some  distance  above  the  base ;  for  in  this  case 
his  lever-arm  will  be  greater,  and  consequently  the  mo- 
ment of  the  force  which  he  exerts.  It  is  familiar  to  every 
one  how  much  is  gained  by  a  long  lever  in  producing  an 
effect ;  that  this  effect  is  increased  not  only  by  increasing 
the  force,  but  also  by  increasing  the  length  of  the  arm 
through  which  it  acts.  Seeing  that  this  was  the  case, 
Archimedes  is  reported  to  have  said  that  with  a  lever 
long  enough  he  could  move  the  world. 

Exercises. — 1.  A  current  flows  east  at  the  rate  of  4  miles  an 
hour,  and  a  vessel  heads  north  at  the  rate  of  10  miles  an  hour :  draw 
a  diagram  showing  the  true  direction  and  velocity  of  the  vessel. 

2.  Four  men  pull  at  a  rope  with  forces  of  40,  50,  25,  and  60  pounds 
in  the  same  direction :  what  is  the  resultant  pull  ?     If  the  two  latter 
pull  in  an  opposite  direction  from  the  others,  what  is  the  intensity 
and  direction  of  the  resultant  ? 

3.  Two  men  carry  a  basket ;  one  pulls  upward  with  a  force  of  20 
pounds,  and  the  other  with  a  force  of  40  pounds:  what  is  their  re- 
sultant and  the  weight  of  the  basket? 

4.  A  body  is  given  simultaneously  three  blows,  one  eastward  at 
the  rate  of  40  feet  per  second,  one  northward,  28  feet  per  second,  one 
westward,  32  feet  per  second  :  which  way  does  it  move,  and  with 
what  velocity  ? 

71.  Work. — Work  consists  in  moving  against  resistance. 
A  horse  or  an  engine  does  work  when  it  pulls  a  load,  a 
bird  when  it  propels  itself  through  the  air,  a  man  when 
he  lifts  up  a  weight. 

Let  us  take  the  latter  case.    When  a  load  is  lifted,  a  cer- 


MOTION  AND   FORCE.  31 

tain  amount  of  work  is  done ;  when  it  is  lifted  twice  as  high, 
twice  as  much  work  is  done,  or  when  the  weight  is  twice 
as  great,  twice  as  much  work  is  done  •  when  twice  as  great 
a  weight  is  lifted  through  three  times  the  height,  six  times 
the  work  is  done ;  or, 

"Work  done  =  weight  X  height. 

In  general,  the  work  done  by  any  force  is  the  product 
of  the  force  and  the  distance  through  which  the  point  of 
application  is  moved. 

72.  Unit  of  Work. — A  unit  of  work  is  the  work  done  in 
raising  a  unit  of  weight  through  a  unit  of  height.     In  the 
English  system  the  units  are  the  foot  and  the  pound,  and 
the  unit  of  work  is  called  the  foot-pound;  in  the  French 
system  the  kilogram  and  metre  are  used,  and  the  unit  of 
work  is  the  kilogram-metre. 

73.  Horse-Power. — For  large  engines  a   larger  unit  is 
used,  the  horse-power.     This  is  equivalent  to  33,000  foot- 
pounds per  minute.1     An  engine  capable  of  lifting  33,000 
pounds  1  foot  in   1  minute,  or  66,000  pounds  1  foot  in  2 
minutes,  or  11,000  pounds  6  feet  in  2  minutes,  is  an  engine 
of  1  horse-power.     Multiply  weight  in  pounds  by  height 
in  feet,  divide  by  the  number  of  minutes  and  by  33,000, 
and  we  have  the  horse-power. 

74.  Erg. — As  these  units  depend  on  gravity,  which  is 
variable,  another,  based  on  the  French  system,  has  been 
employed,  called  the* erg;  the  erg  is  the  work  done  by  a 
force  of  one  dyne  acting  through  one  centimetre. 

Exercises. — 1.  How  many  foot-pounds  of  work  are  done  in  lifting 
20  pounds  through  10  feet  ?  how  many  kilogram-metres  ? 

2.  An  engine  can  lift  2  tons  20  feet  in  40 seconds:  what  is  its  horse- 
power ? 

3.  An  engine  can  lift  20  kilograms  20  metres  in  20  seconds  :  what 
is  its  horse-power  ? 

4.  How  many  ergs  of  work  are  done  by  a  force  of  one  dyne  acting 
through  a  metre? 

5.  A  force  gives  to  a  decagram  of  matter  a  velocity  of  2  centimetres 

1  The  element  of  time  enters  into  horse-power,  but  not  into  foot- 
pounds. 


32  NATURAL   PHILOSOPHY. 

a  second.     If  this  force  acts  through  a  metre,  how  many  ergs  of  work 
are  done  ? 

75.  Energy. — Energy  is  ability  to  do  work.    A  moving 
body  has  this  ability,  hence  it  has  energy.     A  body  lifted 
up  has  this  ability,  hence  it  has  energy.     The  units  of 
energy  are  the  same  as  the  units  of  work. 

76.  Potential  Energy. — A  weight  held  up  by  the  hand 
has  the  power  by  virtue  of  its  position  to  fall,  and  hence  do 
work,  if  its  support  be  withdrawn.     A  body  of  water  held 
up  by  a  dam  has  the  power  to  do  work  on  a  water-wheel, 
if  allowed  to  fall  upon  it.     A  wound-up  spring  has  power 
to  perform  work  in  turning  the   machinery  of  a  clock. 
This  kind  of  energy  is  called  energy  of  position,  or  potential 
energy. 

77.  Actual  Energy. — A  weight  descending,  water  falling 
on  a  wheel,  a  spring  uncoiling,  a  bullet  moving  through 
the  air,  a  muscle  in  use,  have  energy, — energy  of  motion,  or 
actual  energy. 

78.  Formula  for  Potential  Energy. — The  formula  for  potential 
energy  is  w  X  ^,  where  w  represents  the  weight  of  a  body,  and  h  the 
height  to  which  it  is  raised.     For  it  is  evident  that  increasing  either 
of  these  quantities  will  proportionately  increase  the  ability  of  the 
body  to  do  work. 

79.  Formula  for  Actual  Energy. — The  formula  for  actual  en- 
ergy is  £?m>2uwhere  ra  represents  the  mass,  and  v  the  velocity  of  the 
moving  body.     For  its  momentum  is  mv  (Art.  49).     Now,  suppose 
it  to  be  moving  against  a  resistance  which  takes  one  unit  from  its 
momentum  each  second,  it  will  then  require  mv  seconds  to  bring  it  to 
rest,  and  its  mean  velocity  will  be  %v,  for  it  diminishes  uniformly 
from  v  to  nothing.     The  distance  through  which  the  body  would 
move  is  mv  X  \v  =  %mvz.     It  therefore  does  \mvl  units  of  work  upon 
the  resistance  (for  the  resistance  is  supposed  to  be  a  unit  of  force),  and 
its  actual  energy  is  %mvz. 

80.  Energy  of  a  Projectile. — When  a  ball  is  thrown  up- 
ward, its  energy  of  motion  becomes   gradually  less  and 
less,  and  its  energy  of  position  greater  and  greater.     At  its 
highest  point  the  one  is  nothing,  the  other  is  the  greatest 
possible.    During  the  fall  the  conditions  are  reversed.    We 


MOTION  AND   FORCE. 


say  that  the  energy  of  motion  is  converted  into  energy  of 
position  in  the  ascent,  and  converted  back  in  the  descent. 

81.  Potential  and  Actual  Energy  equal. — We  have  proved 

the  two  formulae, — 

Potential  Energy  =  wh. 

Actual  Energy      —$mv*. 

In  the  section  on  falling  bodies  we  will  prove  other  formulae,  which 
will  show  that  the  energy  of  motion  which  a  body  has  at  the  begin- 
ning of  its  ascent  is  just  equal  to  the  energy  of  position  at  its  highest 
point ;  that  is,  that  under  these  conditions  wh  -=  $mv*. 

82.  Conservation  of  Energy. — This  brings  us  to  the  very 
important  doctrine  of  the  conservation  of  energy.    This  says 
that  energy  is  always  conserved  or  preserved ;  that  it  is 
never  destroyed,  but  may  be  converted  into  energy  of  an- 
other form ;  that  the  sum  of  the  energies  of  the  universe, 
like  the  sum  of  the  matter  of  the  universe,  is  constant ;  that 
energy  is  indestructible,  as  matter  is.     We  cannot  follow 
energy  through  all  its  transformations,  any  more  than  we 
can  follow  matter,  but  we  have  the  best  of  grounds  for 
believing  in  the  truth  of  the  theory. 

We  will  show  in  future  chapters  that  heat,  light,  and 
electricity  are  motions  of  the  particles  of  bodies  or  of  the 
ether;  hence  we  have  other  forms  of  energy  in  them. 
These  are  all  convertible,  without  loss,  into  one  another  and 
into  the  two  forms  mentioned  above.  When  a  nail  is  struck 
by  a  hammer,  it  becomes  hot,  for  the  force  of  the  blow  is 
changed  into  heat,  and  sometimes,  when  sparks  are  struck, 
into  light.  When  water  falls  on  a  wheel  from  a  pond,  its 
energy  of  position,  first  converted  into  energy  of  motion, 
moves  the  wheel ;  but  part  of  this  energy  produces  heat 
by  striking  the  wheel,  part  produces  heat  in  the  bearings, 
and  part  runs  the  machinery.  If  an  electrical  machine  be 
connected  with  it,  some  of  the  energy  will  be  converted 
into  electricity  with  its  attendant  light. 

In  a  steam-engine  the  energy  of  position  of  the  mole- 
cules of  coal  is  converted  into  heat,  and  the  heat  finally 
into  motion  of  the  piston. 
c 


34  NATURAL  PHILOSOPHY. 

83.  Correlation  and  Conservation.  —  The  principle  that 
one  force  can  be  converted  into  another  is  the  correlation 
of  forces,  while  the  principle  that  in  this  correlation  no 
energy  is  lost  is  the  conservation  of  energy.  These  are  long 
names,  but  they  express  truths  which  are  of  great  im- 
portance in  modern  science,  and  should  be  thoroughly 
understood. 

Exercises.  —  1.  How  many  foot-pounds  of  energy  of  position  has 
a  weight  of  20  pounds  8  feet  above  the  floor,  with  respect  to  the 
floor  ?  a  table  3  feet  high  stands  on  the  floor  :  how  much  has  the 
weight  with  respect  to  this  table  ?  Ans.  160,  100. 

2.  A  bullet  of  1  ounce  is  shot  from  a  20-pound  gun  with  a  velocity 
of  1600  feet  per  second  :  has  the  motion  of  the  bullet  or  the  recoil  of 
the  gun  greater  energy  ?  and  how  much  ? 

Note.  —  Because  the  momentum  of  the  bullet  equals  the  momentum 
of  the  gun, 

1600  X  xV  =  20  X  velocity  of  recoil. 
Velocity  of  recoil  =  5  feet  per  second. 

W 

Energy  of  motion  =  \  mv2  =  J  —  v2. 

For  the  bullet  =  $  X  oifex  (1600)2  =  2484.  -f  . 


20 

For  the  gun  =  J  X          X  52  =  7.7  +. 


Note.  —  From  this  we  see  the  diiference  between  momentum  and 
energy.  It  is  the  energy,  not  the  momentum,  which  gives  the  power 
to  the  ball  to  penetrate  bodies  and  to  do  harm.  As  we  increase  the 
velocity,  we  increase  the  momentum  in  the  same  proportion,  but  we 
increase  the  energy  in  the  square  ratio.  As  velocity  is  doubled,  mo- 
mentum is  doubled,  but  energy  is  quadrupled.  As  velocity  is  trebled, 
momentum  is  trebled,  but  energy  is  increased  ninefold. 

Perhaps  we  can  understand  this  better  if  we  consider  that  as  it  goes 
twice  as  fast  it  will  meet  twice  as  many  particles  in  the  same  time, 
and  it  will  crowd  them  away  twice  as  fast  ;  that  is,  it  has  four  times 
the  effect  ;  if  it  has  three  times  the  velocity,  it  will  have  nine  times 
the  effect  ;  and  so  on. 

3.  State  what  transformations  of  energy  take  place  in  sliding  a 
body  down  a  plane,  in  the  electric  light,  in  ringing  a  bell,  in  lighting 
a  match,  in  a  clock  running  down,  in  a  pendulum  swinging. 

4.  Which  would  be  preferable,  to  carry  a  40-pound  trunk  up  20 
feet  or  a  60-pound  trunk  up  15  feet  ? 

5.  How  many  pounds  of  water  per  minute  will  a  20  horse-power 
engine  raise  through  200  feet  ?     Ans.  3300. 


MOTION  AND   FORCE,  35 


GKAYITY  AND  STABILITY. 

84.  Effects  of  Attraction, — The  earth  attracts  every  par- 
ticle of  matter  towards  itself.  This  gives  us  the  phenom- 
ena of  falling  bodies,  causes  matter  to  have  weight,  makes 
the  surface  of  still  water  level,  and  constantly  operates  in 
many  ways  we  do  not  notice. 

f     85.  How  Attraction  Acts. — It  does  not  require  any  time 
•'I  for  this  force  to  act.     Attraction  traverses  the  great  space 
Ibetween  the  sun  and  the  earth,  to  the  best  of  our  knowledge, 
instantaneously.     Nor  does  the   interposition  of  another 
body  affect  it  in  any  way.     We  can  cut  off  sound  or  heat 
or  light  by  the  interposition  of  a  wall,  but  attraction  acts 
through  it  without  diminution.    Nor  does  the  kind  of  mat- 
ter make  any  difference.     Every  molecule  is  attracted  alike, 
the  number  of  molecules  determining  the  total  attraction. 

86.  Law  of  Attraction. — The  law  of  gravity,  which  was 
discovered  by  Newton,  is  that  every  portion  of  matter  in  the 
universe  attracts  every  other  portion  with  a  force  directly  pro- 
portional to  the  masses,  and  inversely  proportional  to  the  square 
of  the  distance  between  them. 

Questions. — How  much  is  the  attraction  between  two  masses 
changed  by  doubling  the  distance  between  them  ?  by  increasing  it  5 
times?  by  doubling  one  mass?  by  doubling  one  mass,  trebling  the 
other,  and  trebling  the  distance  between  them  ? 

87.  Decrease   of    Gravity  Downward. — The    gravity  is 
greatest  at  the  surface  of  the  earth.     When  we  go  down 
into  the  earth  the  gravity  decreases,  because  some  of  the 
matter  of  the  earth  is  attracting  us  upward.     Were  we  to 
get  half-way  to  the  centre  we  should  only  have  half  the 
weight  that  we  have  at  the  surface.    At  the  centre  we  should 
have  no  weight,  being  equally  attracted  in  all  directions. 

Were  it  possible  for  a  body  to  fall  freely  towards  the 
centre,  it  would  increase  its  velocity  continually  and  fly  to 
the  surface  on  the  other  side,  thence  back  again.  Were 
there  no  resistance,  this  would  go  on  forever.  Otherwise, 


36  NATURAL  PHILOSOPHY. 

the  vibrations  would  become  smaller  and  smaller,  and  the 
body  would  finally  settle  at  the  centre. 

88.  Centre  of  Gravity. — The  centre  of  gravity  of  a  body 
is  the  point  about  which  it  will  balance  in  every  position. 
If  a  body  has  a  uniform  figure  and  the  same  structure 
throughout,  the  centre  of  gravity  is  in  t.he  centre  of  the 
figure,  and  is  readily  found.     The  centre  of  gravity  of  a 
homogeneous  sphere  is  at  its  centre ;  of  a  cylinder,  at  the 
centre  of  its  axis ;  of  a  uniform  ring,  not  in  the  mass  of  the 
ring,  but  in  the  space  in  the  centre  ;  of  a  rectangular  block, 
where  its-  diagonals  intersect. 

89.  How  to  find  the  Centre  of  Gravity.— If  a  body  is  hung 

up  by  a  string,  the 
centre  of  gravity 
will  be  in  the  line 
of  the  string  pro- 
longed  down- 
ward.  If  a  new 
point  of  suspen- 
sion be  taken, 
and  the  line  pro- 

Fia.  17. — CENTRE  OF  GRAVITY.  , 

longed  down- 
ward, it  will  cut  the  first  line  in  the  centre  of  gravity. 
This  enables  us  to  find  the  centre  of  gravity  in  certain 
cases.  In  the  case  of  a  thin  body,  we  may  balance  it  over 
a  ruler  in  two  directions,  or  over  the  edge  of  a  table,  as  in 
Fig.  17.  If  the  lines  of  the  ruler  or  the  edge  of  the  table  be 
marked  on  it,  their  intersection  will  be  the  centre  of  gravity. 
In  general,  its  position  has  to  be  found  mathematically. 

Experiment  13. — Lay  a  thin  board  on  a  ruler,  and  find  its  centre 
of  gravity  as  described.  Bore  a  hole  here  and  insert  an  awl.  Notice 
how  the  board  is  balanced  in  every  position. 

Experiment  14. — Bore  a  hole  in  a  board,  and  insert  an  awl,  on 
which  hang  a  plumb-line.  Mark  the  path  of  the  line  on  the  board. 
Do  this  again  from  some  other  point.  The  intersection  of  the  lines 
is  the  centre  of  gravity. 

90.  Representation  of  Weight  as  a  Force. — A  line  down- 


MOTION  AND  FORCE.  37 

ward  from  the  centre  of  gravity  of  a  body  may  represent 
its  weight;  that  is,  it  will  be  the  resultant  of  all  the 
parallel  pulls  of  the  earth  on  its  different  particles.  Hence 
in  treating  of  the  weight  of  a  body  as  a  force  we  must 
represent  it  by  a  line,  in  the  direction  of  a  plumb-line, 
downward  from  its  centre  of  gravity. 

91.  Base  of  Support  and  Centre  of  Gravity. — If  a  body 
rests  on  a  support,  and  a  line  from  the  centre  of  gravity 
downward  meets  this  support  within  the  base  of  the  body, 
it  will  remain  in  position ;  if  not,  it  will  slide  or  overturn, 
for  the  downward  pull  meets  with  no  resistance. 

Experiment  15. — Find  the  centre  of  a  board,  as  in  Experiment  14. 
Tilt  it  sidewise,  and  notice  that  when  the  centre  is  exactly  over  the 


FIG.  18.  —  CENTRE  OF       FIG.  19. — CENTRE  OF  GRAVITY. 
GRAVITY  AND  BASE  OF 
SUPPORT. 

point  of  support  a,  as  indicated  by  a  plumb-line,  the  body  is  just 
ready  to  turn  either  way. 

Experiment  16. — Place  a  light  piece  of  stick,  a£>,  with  one  end 
resting  on  a  table.  At  b  notch  it  so  that  another  stick,  be,  may  fit  in 
the  notch  and  press  against  the  handle  of  a  bucket  under  the  table. 
A  string,  cd,  must  also  be  attached  to  the  handle.  A  great  weight 
may  now  be  placed  in  the  bucket,  for  the  centre  of  gravity  of  the 
weight  comes  under  the  support  at  a.  If  b  is  depressed,  it  raises  the 
centre  of  gravity,  and  hence  b  is  again  quickly  raised. 

A  wagon  at  rest  will  overturn  when  the  line  drawn 
from  the  centre  of  gravity  falls  outside  the  wheels.  The 
tower  of  Pisa  *  could  be  made  to  overturn  by  building  it 
higher,  for  the  centre  of  gravity  would  thus  be  thrown 
farther  out. 

When  a  man  stands  erect,  the  line  from  his  centre  of 

1  Where  is  this,  and  how  constructed? 
4 


38 


NATURAL   PHILOSOPHY. 


gravity  falls  between  his  feet.     In  beginyiing  to  walk,  he 
throws  his  body  forward,  so  as  to  bring  his  centre  of  gravity 


FIG.  20. — LINE  FROM  CENTRE  OF  GRAVITY  MUST  FALL  INSIDE  THE  WHEELS. 

in  front  of  his  feet.  He  would  now  fall  did  he  not  catch 
himself  by  throwing  one  foot  forward.  The  operation  is 
then  repeated  with  the  other  foot.  He  also  throws  his 
body  from  side  to  side,  so  as  to  keep  the  centre  of  gravity 
over  the  foot  which  is  on  the  ground.  In  carrying  a 


FIG.  21.— UNSTABLE,  NEUTRAL,  AND  STABLE  EQUILIBRIUM. 

weight  on  his  back,  he  leans  forward,  and  in  carrying  it 
in  one  hand  he  leans  sidewise,  for  the  same  reason. 

92.  Stability. — The  position  of  a  body  is  stable  when  any 


MOTION  AND  FORCE.  39 

overturning  force  beginning  to  act  will  tend  to  cause  its 
centre  of  gravity  to  rise,  as  a  brick  lying  flat  ;  for  then  it  will 
of  itself  return  to  its  original  position  when  the  force  is 
withdrawn.  It  is  unstable  when  the  slightest  overturning 
force  causes  its  centre  of  gravity  to  fall,  as  a  cane  bal- 
anced on  end,  in  which  case  it  will  not  recover  its  position, 
but  will  go  farther  from  it.  It  is  neutral  when  the  over- 
turning force  causes  motion  in  a  horizontal  line,  as  a  ball  on 
a  floor;  then  it  will  come  to  rest  in  any  position. 

93.  Measure  of  Stability.—  The  more  the  centre  of  gravity 
has  to  rise  in  overturning,  the 
more  stable  the  body  is.  A  brick 
on  its  flat  side  is  more  stable 
than  a  brick  on  end.  To  over- 
turn it  the  centre  of  gravity  has 
to  be  raised  through  the  verti- 


cal height  ab,  which  is  a  much  Fm  22-_STABIUTY. 

greater  distance  in  one  case  than 

in  the  other,  and  therefore  a  much  greater  force  is  required. 
The  work  done  in  overturning  is  the  weight  multiplied 
by  ab. 

Exercises.  —  1.  When  will  a  body  slide,  and  when  roll,  down  an 
inclined  plane? 

2.  In  rising  from  a  chair,  why  do  we  lean  the  body  forward  ? 

3.  Why  is  it  easier  to  walk  on  a  fence  with  a  long  stick  in  the 
hand? 

4.  When  is  a  pendulum  in  stable  equilibrium  ? 

5.  A  cone  balanced  on  its  apex  is  in  what  kind  of  equilibrium  ? 
on  its  base  ?  on  its  side  ? 

6.  Why  cannot  a  person  pick  up  an  object  from  the  floor  in  front 
of  him  when  standing  with  his  heels  against  a  vertical  wall  ? 

7.  Should  the  centre  of  gravity  of  a  ship  be  high  or  low  ?  of  a 
wagon  ? 

8.  Why  is  it  easier  to  suspend  an  iron  ring  on  a  nail  on  the  inside 
than  to  balance  it  on  the  outside  ? 

9.  What  would  a  200-pound  man  weigh  if  moved  to  within  1000 
miles  of  the  centre  of  the  earth  ?     Ann.  50  pounds. 


40  NATURAL  PHILOSOPHY. 


FALLING  BODIES. 

94.  How  much  a  Body  will  Fall  in  a  Second. — The  attrac- 
tion of  the  earth  is  such  that  it  will  cause  a  body  starting 
from  rest  to  fall  about  16.1  feet  (about  4.9  metres)  in  one 
second.  Its  velocity  at  the  beginning  was  nothing,  and  it  in- 
creased uniformly  during  the  second.  Hence  at  the  end  it 
is  moving  at  the  rate  of  32.2  feet  (9.8  metres)  ;  that  is,  it 
has  acquired  a  velocity  which  if  continued  uniformly  would 
carry  it  over  32.2  feet  (9.8  metres)  the  second  second.  But 
during  this  second  second  it  has  also  the  pull  of  the  earth, 
adding  16.1  feet  more  to  the  space  passed  over,  making 
48.3  feet,  or  three  times  16.1  feet,  in  that  second.  The  third 
second  it  has  an  acquired  velocity  of  64.4  feet,  and  an 
additional  pull  of  16.1  feet,  making  80.5  feet,  or  five  times 
16.1  feet,  as  the  fall  during  the  third  second. 

In  general,  the  fall  through  any  second  is  found  by 
taking  the  series  of  odd  numbers,  1,  3,  5,  7,  etc.,  and  mul- 
tiplying 16.1  by  the  number  in  the  series  corresponding  to 
the  given  second. 

Let  it  be  required  to  find  the  fall  during  the  sixth  sec- 
ond.    The  sixth  number  of  the  series  is  11. 
11  X  16.1  =  177.1  feet. 

The  space  fallen  through  in  the  first  three  seconds  will 
evidently  be  (1  -f  3  -f  5)  X  16.1 ;  in  the  first  five,  (1  +  3 
_j_  5  _f_  7  _|_  9)  x  16.1 ;  and  so  on. 

The  sum  of  the  numbers  in  the  parenthesis  is  found  by 
adding  the  end  terms,  and  multiplying  by  half  the  number 
of  terms,  or  the  number  of  seconds.1 


1  If  the  ninth  second  is  given,  we  find  the  odd  number  correspond- 
ing by  multiplying  9  by  2  and  subtracting  1.  If  we  add  the  first 
two  odd  numbers,  it  gives  the  square  of  2  ;  if  the  first  three,  the 
square  of  3;  and  so  on.  Thus,  1  +  3  =  4,  1  +  3  +  5  =  9,  1  +  3  +  5 
+  7  =  16.  We  thus  see  a  reason  for  the  rule,  to  be  announced  farther 
on,  that  the  spaces  passed  over  vary  as  the  squares  of  the  times. 


MOTION  AND   FORCE.  41 

To  find  the  space  through  which  a  body  would  fall  in  nine 
seconds,  we  add  the  end  terms  1  and  17,  and  multiply  by  -| 
and  by  16.1,  or 

(17  +  1)  X  f  X  16.1  =  1304.1  feet. 
95.  Formulae  for  Falling  Bodies. — But  it  is  better  to 
work  out  some  general  formulas. 

Let  s  represent  the  space  passed  over ; 
"   t        "  "    time; 

"  v        "  "    velocity; 

"  g        "  "    acceleration  produced  by  gravity  in 

one  second  =  32.2  feet  =  9.8  metres,  which  is  taken  as  the 
measure  of  gravity.  As  g  is  the  velocity  acquired  in  one 
second,  in  t  seconds  we  will  have 

v  =  gt.  (1) 

But  as  the  velocity  uniformly  increases  from  nothing  to 
gtj  the  mean  velocity  is  J  gt,  and  the  space  passed  over  in 
t  seconds  with  this  velocity  is 

«  =  }0fX*  =  Iff?.  (2) 

From(l),  t=l  (3) 

Substitute  in  (2), 

«  =  l<rxjH»or  (4) 

(5) 


From  (2) 

9 

Note. — We  said  (page  33)  that  the  potential  energy  which  a  hody 
has  when  raised  above  a  plane  is  equal  to  the  actual  energy  of  its 
motion  when  it  falls  to  that  plane ;  in  other  words,  that 

ws  =  \mvi. 

We  can  now  prove  this.  The  weight  of  a  hody  is  equal  to  the 
number  of  its  particles  multiplied  by  the  pull  on  each,  or 

w  =  mg. 

Also,  from  (4),  s=--. 

Multiplying  these  together,  we  have  ws  —  trig  Xs~—  £wv2)  which 

is  what  we  wanted  to  prove. 

4* 


42  NATURAL  PHILOSOPHY. 

These  formulsB  enable  us  to  work  out  all  possible  cases 
of  falling  bodies.  We  seek  for  one  in  which  the  desired 
quantity  constitutes  the  first  member,  and  in  which  the 
last  member  is  all  known. 

Exercises. — 1.  How  far  will  a  body  fall  in  8  seconds?  We  want 
s,  and  have  given  t  and  g :  hence  use  formula  (2). 

2.  How  long  will  it  take  a  body  to  fall  through  200  metres  ?     Use 
(6). 

3.  What  velocity  would  a  body  acquire  in  each  of  the  last  cases  ? 

4.  A  body  has  a  velocity  of  400  feet  per  second :  through  what 
space  and  how  long  has  it  been  falling? 

5.  A  body  has  a  velocity  of  40  metres  a  second :  through  what 
space  and  how  long  has  it  been  falling? 

96.  Projection  Upward. — When  a  body  is  projected  up- 
ward, the  attraction  of  the  earth  takes  away  from  its 
energy  of  motion,  and  when  it  falls  it  gives  it  back  again. 
It  has  the  same  velocity  in  coming  down  that  it  had  in 
going  up  at  the  same  height.  The  circumstances  of  the 
motion  are  just  reversed. 

1.  How  high  will  a  body  rise  by  an  upward  impulse  of  80  metres 
per  second  ? 

Use  formula  (4). 

6400 


2.  A  bullet  is  shot  up  with  a  velocity  of  1600  feet  per  second  :  how 
high  will  it  go? 

3.  A  body  rises  to  the  height  of  300  metres :  how  long  did  it  take  it  ? 

97.  Resistance  of  Air. — All  the  above  is  on  the  supposi- 
tion that  the  motion  is  in  a  vacuum.     The  resistance  of 
the  air  very  materially  alters  the  results  in  real  cases.     A 
body  will  not  rise  as  high  as  it  otherwise  would,  nor  will 
it  fall  with  nearly  the  velocity  with  which  it  was  projected. 

98.  Parabola  of  a  Projectile. — In  the  case  of  bodies  pro- 
jected not  vertically,  were  there  no  resistance  the  body 
would  move  in  a  symmetrical  curve  called  a  parabola*  and 

1  A  parabola  is  a  curve  every  point  of  which  is  equally  distant 
from  a  point/,  Fig.  24,  and  from  a  straight  line  ec.     When  a  gun  is 


MOTION  AND  FORCE. 


43 


would  have  equal  velocities  at  equal  heights.  In  practice, 
it  descends  more  steeply  than  it  rises.  The  curve  is  some- 
thing like  that  represented  in  Fig.  23. 


FIG.  23.— CURVE  OF  A  BALL. 


Fro.  24.— PARABOLA. 


Experiment  17. — Get  one  of  your  friends  to  knock  a  ball,  and 
take  a  side  view  of  the  curve. 

If  a  body  were  projected  horizontally  from  the  top  of  a 
tower,  it  would  reach  the  level  at  the 
same  time  as  if  it  were  dropped. 
Moreover,  it  would  reach  the  level 
at  the  same  time  whatever  its  ve- 
locity of  projection.  For  gravity 
is  the  only  downward  force  acting, 
and  a  horizontal  impulse  will  not 
change  the  circumstances  of  its 
motion  vertically.  It  is  a  general 
law  that  a  force  at  right  angles  to  the  motion  of  a  body 
cannot  change  its  velocity,  though  it  may  its  direction. 

The  range,  bd,  of  a  projectile  is  equal  to  the  velocity  of 
discharge  multiplied  by  the  time  it  is  moving.  For  the 
discharge  is  caused  by  an  impulsive  force,  which  tends  to 
produce  uniform  velocity.  Gravity  acting  at  right  angles 
does  not  cause  any  change  in  this  horizontal  velocity.  The 
projectile  moves  faster,  but  it  does  not  get  along  in  a  hori- 
zontal direction  any  faster  in  one  part  of  its  flight  than  in 


FIG. 


25.  — PROJECTION 

ZONTALLY. 


shot  horizontally,  the  curve,  except  for  the  resistance  of  the  air,  would 
be  a  semi-parabola,  ab. 


44  NATURAL  PHILOSOPHY. 

another.     The  same  is  true  if  it  be  projected  from  the 
ground  at  an  angle  upward. 

THE   PENDULUM. 

99.  What  is  a  Pendulum  ?— The  pendulum  is  a  body  sus- 

pended by  a  flexible  cord,  so  that  it  may 
freely  vibrate.  When  drawn  aside  from 
a  vertical  line,  the  weight  is  raised  and 
gravity  causes  it  to  descend.  Its  inertia 
will  then  carry  it  up  the  other  side,  and 
were  it  not  for  friction  and  the  resistance 
of  the  air  it  would  rise  to  the  height  from 
which  it  fell,  and  swing  back  and  forth 
forever.  On  account  of  these  resistances 
,,,  9R  p  .  it  does  not  rise  so  high,  but  makes  shorter 

HIQ.  Zb. — PENDULUM. 

and    shorter  vibrations,   and   is    finally 
brought  to  rest. 

100.  Energy  of  a  Pendulum. — "When  drawn  aside,  it  has 
energy  of  position  equal   to  its  weight  multiplied  by  ab  ; 
this  is  converted  into  energy  of  motion  in  the  fall,  and  this 
is  reconverted  to  energy  of  position  in  the  ascent,  except 
such  portion  of  it  as  appears  as  heat  in  point  of  suspension 
and  in  the  air.     Finally  the  whole   energy  is  converted 
into  heat,  and  the  pendulum  remains  at  rest. 

101.  Simple  Pendulum. — The  laws  of  pendulums  are  in- 
vestigated mathematically  by  considering  an  ideal  pendu- 
lum of  which  the  bob  is  a  single  point  without  size,  yet 
with  weight,  and  the  string  perfectly  inelastic  and  without 
breadth,  the  whole  moving  without  any  resistance.     This 
arrangement  is  called  a  simple  pendulum.     The  real  pendu- 
lum, the  compound  pendulum,  approaches  in  its  motions  to 
this.     The  longer  and  finer  the  string,  the  more  nearly  do 
its  motions  conform  to  those  of  the  simple  pendulum. 

102.  Equation  Of  Pendulum. — The  following  equation  has  been 
found  to  give  the  circumstances  of  the  motion  of  a  simple  pendulum  : 


MOTION  AND  FORCE.  45 


In  which 

T=  time  of  complete  vibration  ; 
1=2  length  of  pendulum  ; 
g  —  force  of  gravity  ; 

it  =  3.1416  =  ratio  of  circumference  to  diameter  of  a  circle. 
From  this  equation1  we  have  the  following  laws  : 

103.  Laws  of  the  Pendulum. — 1.  The  times  of  all  pendulums 
of  the  same  length  at  the  same  place  are  independent  of  the  ex- 
tent of  the  vibration.  A  long  swing  will  be  performed  in 
nearly  the  same  time  as  a  short  one. 

This  is  only  approximately  true  in  the  case  of  the  or- 
dinary pendulum ;  a  pendulum  can  be  so  arranged  that  it 
will  be  strictly  true. 

2.  The  times  of  different  pendulums  at  the  same  place  are 
proportional  to  the  square  roots  of  their  lengths.     The  time  of 
vibration  of  a  pendulum  four  times  as  long  as  another  is 
twice  as  great. 

3.  The  times  of  pendulums  of  the  same  length  are  inversely 
proportional  to  the  square  root  of  the  intensity  of  gravity. 

To  find  the  intensity  of  gravity  at  any  place,  we  should 
measure  the  length  of  a  pendulum,  count  the  time  of  its 
vibration,  and  then  in  the  formula  T=7ti/^  we  have  all 
the  terms  but  g,  which  may  be  readily  found.  This  sup- 
poses that  we  have  a  simple  pendulum.  If  we  have  a 
compound  pendulum,  we  must  exhaust  the  air  around  it, 
diminish  the  friction  at  its  point  of  support,  increase  the 
flexibility  of  the  cord  as  much  as  possible,  and  make  cer- 
tain allowance  for  the  size  of  the  bob. 

These  laws  are  independent  of  the  nature  of  the  mate- 
rial of  the  bob. 

Experiment  18. — Procure  pendulums  made  of  some  heavy  mate- 
rial, as  lead,  suspended  by  long  silk  cords  to  the  ceiling. 


1  The  equation  is  proved  by  Higher  Mathematics. 


46 


NATURAL   PHILOSOPHY. 


1.  Take  two  of  them  of  the  same  length,  draw  one  aside  farther 
than  the  other,  and  let  them  go  at  the  same  instant.     Notice  the 
equality  of  their  times.     Or  take  a  long  pendulum  and  count  its  vi- 
brations in  a  minute  when  the  vibrations  are  long  and  when  they  are 
short. 

2.  Make  one  just  four  times  as  long  as  the  other  ;  notice  that  the 
short  one  swings  twice  while  the  long  one  swings  once. 

3.  Change  the  length  till  you  have  it  vibrating  once  in  a  second; 
measure  this  length,  and  compare  it  with  that  obtained  from  the 
formula  by  making  T=  1,  #  =  32.2,  and  TT=  3.1416. 

A  pendulum  which  vibrates  once  in  a  second  is  called  a  seconds 
pendulum. 

104.  Pendulum  for  Clocks. — The  utility  of  a  pendulum 
for  clocks  may  be  explained  by  Fig.  27.  The  pendulum 
swings  between  two  arms  a,  and  is  connected  with  the 
rod  o  and  the  escapement  mn.  The  pallets 
of  this  work  into  the  teeth  of  the  escape- 
ment-wheel E.  When  the  pendulum  swings, 
one  of  the  teeth  of  the  wheel  escapes  from 
the  pallet  m,  and  the  weight,  which  acts 
on  R,  falls  a  little,  and  moves  the  train  of 
machinery.  But  directly  the  pallet  n 
catches  and  holds  it  again.  So  the  pendu- 
lum simply  regulates  the  motion  of  the 
machinery.  Swift  vibrations  make  the 
clock  go  faster,  and  slow  vibrations  make 
it  go  slower.  As  a  long  pendulum  swings 
slower  than  a  short  one,  by  lengthening 
the  pendulum  the  rate  of  the  clock  is  di- 
minished, and  vice  versa.  As  heat  pro- 
duces this  result  in  a  metal  bar,  it  is  neces- 
sary to  compensate  for  this.  This  may  be 
done  by  a  gridiron  pendulum  so  arranged 
that  when  some  of  the  bars  expand  down- 
ward and  lengthen  the  pendulum,  the 
others  expand  upward  and  shorten  it.  By 
making  these  of  different  materials  the 
expansion  in  one  direction  may  be  made 
just  to  balance  that  in  the  other. 


FIG.  27.— PENDULUM 
BOR  CLOCKS. 


MOTION  AND   FORCE. 


47 


MACHINES. 

105.  The  Mechanical  Powers. — All  machines,  however 
complex,  are  combinations  of  one  or  more  of  the  six  me- 
chanical powers, — viz.,  the  lever,  wheel  and  axle,  pulley,  in- 
clined plane,  wedge,  and  screw. 

THE   LEVER. 

106.  The  Lever. — The  lever  is  a  bar  which  can  be  turned 
about  a  support.    This  support  is  called  the  fulcrum.    The 
power  and  the  weight  act  on  this  bar  at  different  points. 
The  relative  positions  of  fulcrum,  power,  and  weight  deter- 
mine the  kind  of  the  lever. 


Fia.  29. — LEVER  OF  THE  SECOND  KIND. 


107.  Kinds  of  Lever. — A  lever  of  the  first  kind  has  the 


48 


NATURAL  PHILOSOPHY. 


fulcrum  between  the  power  and  the  weight,  as  in  a  steel- 
yard or  a  crow-bar. 

A  lever  of  the  second  kind  has  the  weight  between  the 
power  and  the  fulcrum,  as  in  a  nut-cracker  or  an  oar,  or  in 
a  crow-bar  used  as  in  Fig.  29. 


FIG.  30.— LEVER  or  THE  THIRD  KIND. 

A  lever  of  the  third  kind  has  the  power  between  the 
weight  and  the  fulcrum,  as  in  the  treadle  of  a  lathe. 

Questions. — What  kind  of  lever  is  a  balance  ?  a  see-saw  ?  a  pair 
of  scissors  ?  a  ladder  raised  by  a  man  near  its  base  ?  the  forearm  of  a 
man  ?  a  pair  of  tongs  ?  pincers  ?  a  wheelbarrow  ?  sheep-shears  ?  the 
handle  of  a  water-pump  ?  a  claw-hammer  used  in  drawing  a  nail  ? 
the  rudder  of  a  ship  ? 

Where  is  the  fulcrum  in  each  case  ? 

108.  law  of  the  Lever. — The  law  of  the  lever  in  equi- 
librium is  that  the  moment  of  the  power  is  equal  to  the 
moment  of  the  weight ;  that  is  (Figs.  28,  29,  30), 
p  x  ab  =  w  X  <w. 

In  this  equation,  if  we  know  any  three  terms,  the  re- 
maining one  can  be  found. 


MOTION  AND   FORCE.  49 


Exercises. — 1.  Given  p  =  20,  ab  =8,  ac  =  6.     Find  w. 

2.  Given  p  =  18,  ab  =  8,  w  =  240.     Find  ac. 

3.  Given  JB  =  5,  w  =-  200,  aft  =  400.     Find  ac. 

4.  Given  ab  =  40,  ac  =  80,  w  =  200.     Find  p. 

5.  Given  ac  =  20,  p  =  2,  10  =  50.     Find  length  of  lever. 

Experiment  19.— Take  a  rod  and  mark  it  off  in  inches.  Place  a 
fulcrum  near  one  end,  and  a  5-pound  weight  2  inches  from  the  ful- 
crum. Balance  it  with  a  1-pound  weight.  It  will  have  to  be  just 
10  inches  from  the  fulcrum.  Vary  the  weights  and  the  distances. 

109.  Ratio  of  Power  and  Weight. — Whenever  the  lever- 
arm  of  the  uower  is  greater  than  the  lever-arm  of  the 
weight,  the  power  is  less  than  the  weight.     In  levers  of  the 
first  kind  the  power  may  be  greater  or  less  than  the  weight ; 
in  the  second  kind  it  is  always  less ;  and  in  the  third  kind 
it  is  always  greater. 

110.  Spaces  vary  inversely  as  Forces. — The  space  through 
which  the  power  and  weight  act  is  always  proportioned  to 
their  lever-arms,  and  hence  in  inverse  ratio  to  their  mag- 
nitudes.    In  order  to  lift  w  tow?,p  has  to  move  toy,  a  dis- 
tance just  as  many  times  greater 

than  ww'  as  w  is  greater  than  », 

,, 
or  as  ap  is   greater  than  aw. 

We  gain  power,  but  we  have  to 
move  through  a  greater  space 
and  with  greater  velocity.  It  FIG.  SI.—THE  LEVEE. 

is  a  general  law  in  machinery 

that  the  distances  through  which  the  power  and  the 
weight  move  are  inversely  proportional  to  their  magni- 
tudes, and  since  by  "  work  done"  we  mean  the  force  mul- 
tiplied by  the  distance  through  which  it  moves,  we  have 
another  law  for  the  lever, — the  work  done  by  the  power  is 
equal  to  the  work  done  by  the  weight. 

111.  The  Balance. — The  balance  is  a  lever  of  the  first 
kind.     Its  accuracy  will  depend  on  the  exact  equality  of  the 
two  arms,  and  may  be  tested  by  first  weighing  a  substance, 
then  reversing  weights  and  substance.     If  they  still  bal- 
ance, it  is   correct.      By  its   sensitiveness  we   mean  the 

c       d  5 


50 


NATURAL   PHILOSOPHY. 


amount  of  weight  which,  placed  in  either  pan,  after  being 
exactly  balanced,  will  cause  it  to  turn.     The  smaller  this 

weight,  the  more  sen- 
sitive it  is.  The  sensi- 
tiveness is  increased  by 
diminishing  friction  at 
the  points  of  turning, 
by  placing  the  centre 
of  gravity  of  the  beam 
near  the  point  of  sup- 
port, and*  by  making 
the  beam  long  and 
light.  The  first  is  ac- 
complished by  making 
the  fulcrum  of  a  piece 
Fio.32.-THE  BALANCE.  of  steel  called  a  knife- 

edge. 

112.  Bent  Levers. — If  the  lever  is  bent,  and  the  forces  are  not 
parallel,  the  general  law  still  holds.   But  we  must  measure  the  lever- 


Fia.  33. — ARM  OF  A  DELICATE  BALANCE. 


arms  from  the  fulcrum  perpendicular  to  the  direction  of  the  force. 
In  the  figure  (34)  the  arms  are  ab  and  ac. 


U  m  v  c.noi  i  i    w» 

DEPARTMENT  OF  PHYSICS 


MOTION  AND  FORCE. 


51 


113.  Compound  Levers.— If  one  lever  acts  on  a  second,  as  in 
Fig.  35,  the  power  of  the  second  lever  is  the  weight  of  the  first.     If 


FIG.  34.— BENT  LEVEE. 


FIQ.  35.— COMPOUND  LEVEE. 


a6  =  6,  ac  =  2,  cd=5,  de=l,  and  a  power  of  10  is  applied  at   b. 
Then  in  the  first  lever, 

6  X  10  =  2  X  weight  at  c. 

Weight  at  c  —  30. 
And  in  the  second  lever, 


This  is  also  obtained  by  multiplying  the  power  by  the  product  of 
the  lever-arms  of  the  powers  and  dividing  by  the  product  of  the  lever- 
arms  of  the  weights,  or 

10X6X5-^-2X1=150. 

THE  WHEEL   AND  AXLE. 

114.  The  Wheel  and  Axle.  —  The  principle  of  the  wheel 
and  axle  is  the  same  as  that  of 
the  lever. 

The  radius  of  the  wheel  ab  is 
the  lever-arm  of  the  power,  and  the 
radius  of  the  axle  ac  is  the  lever- 
arm  of  the  weight.  There  is  equi- 
librium when 

p  x  ab  =  w  X  ac. 
Having  given  any  three  of  these, 
the  fourth  can  be  found  as  in  the 
case  of  the  lever. 

The  power  is  applied  by  means 
of  a  handle,  or  of  a  cord  wrapped  around  the  wheel,  and  the 


Fio.  36. — WHEEL  AND  AXLE. 


52 


NATURAL  PHILOSOPHY. 


weight  is  attached  by  a  cord  around  the  axle.  The  power 
may  act  at  any  angle  with  the  line  of  the  weight,  as  p',  so 
that  the  wheel  and  axle  is  used  for  the  transmission  of  force 


FIG.  37.— WINDLASS. 


FIG.  38.— CAPSTAN. 


in  different  directions.  If  they  are  of  the  same  diameter, 
there  is  nothing  gained  except  the  change  of  direction. 

The  windlass  (Fig.  37)  and  capstan   (Fig.  38)  are  ex- 
amples of  the  wheel  and  axle. 

115.  Cog- Wheels, — If  the  wheel  or  the  axle  has   teeth  which 

work  into  similar  teeth  in  other 
wheels,  we  will  have  a  train  of 
cog-wheels.  The  law  of  equi- 
librium of  such  a  train  is :  the 
weight  multiplied  by  the  product 
of  all  the  radii  of  the  axles  is 
equal  to  the  power  multiplied  by 
the  product  of  all  the  radii  of  the 
wheels. 

Since  the  teeth  of  a  small  wheel 
are  the   same   distance  from  one 
FIG.  39.— TEAIN  OF  WHEELS.  another  as  the  teeth  of  a  larger 

wheel  in  which  it  works,  when  it 

makes  a  complete  revolution  the  larger  one  has  only  turned  part 
way  round.  If  one  has  half  as  many  teeth  as  the  other,  it  will  make 
two  revolutions  to  one  of  the  other.  It  will,  therefore,  travel  twice 
as  fast.  But  the  number  of  teeth  is  proportional  to  the  circumfer- 
ences, and  hence  to  the  radii,  of  the  wheels.  Hence  we  have  the  prin- 


MOTION  AND  FORCE.  53 

ciple  that  the  velocity  of  connected  wheels  is  inversely  proportional 
to  their  radii. 

116.  Train  Of  Wheels. — An  axle  with  cogs  is  called  a  pinion. 
If  a  power  turns  a  wheel  the  pinion  of  which  works  in  another  wheel, 
the  pinion  of  this  in  another  wheel,  and  so  on,  we  have  great  increase 
of  power,  but  we  lose  velocity.     If  we  apply  our  power  to  the  other 
end  of  the  train,  the  last  wheel,  we  gain  great  velocity  when  we  reach 
the  first  pinion,  but  we  lose  power  in  the  same  proportion.     The  first 
method  is  used  when  we  want  a  small  power  to  move  a  heavy  weight, 
and  the  latter  when  we  want  to  gain  a  great  velocity. 

Wheels  may  also  be  connected  by  means  of  belts.  The  circum- 
stances of  motion  are  the  same  as  in  a  train  of  cog-wheels.  In  this 
case  the  friction  between  the  belt  and  the  surface  of  the  wheel  takes 
the  place  of  the  cogs,  and  the  advantage  is  that  power  can  be  commu- 
nicated through  a  long  distance. 

Exercises. — In  the  following  examples  let  R  stand  for  the  radius 
of  the  wheel  and  r  for  the  radius  of  the  axle. 

1.  Given  R  =  20,  r  =  5,  and  P=  200,  to  find  W. 

2.  Given  R  =  20,  P=  100,  and  W=  1000,  to  find  r. 

3.  Given  R  =  20,  r  =  $,  and  W=  500,  to  find  P. 

4.  Given  r  =  \,  W=1QQO,  and  P=40,  to  find  R. 

5.  In  lifting  an  anchor  which  weighs  1000  pounds,  four  men  work 
a  capstan  having    a  radius   of   2  feet,  by  bars  the  outer  ends  of 
which  are  6  feet  from  the  centre  of  the  barrel.    How  much  force  does 
each  exert  ?     Ans.  83.3+  pounds. 

6.  A  power  of  5  pounds  acts  on  a  wheel  with  a  radius  of  1  foot. 
The  pinion  (2  inches  radius)  acts  in  a  wheel  of  1  foot  radius.     This 
is  repeated  3  times.     "What  weight  may  be  lifted  ?  Ans.  1080  pounds 

THE   PULLEY. 

117.  Fixed  Pulley. — The  pulley  consists  of  a  wheel  work- 
ing in  a  block.     In  its  simplest  form  it  is  used  to  change 
the  direction  of  a  force.     In  this  case  there  is  no  power 
gained ;  a  little  is  lost  by  friction  and  by  the  rigidity  of 
the  rope ;  but,  except  these,  it  is  carried  over  without  loss 
or  gain.     In  the  figure  the  downward  force  becomes  an 
upward  one,  and  can  be  applied  to  lifting  weights.     Such 
a  pulley  is  called  a  fixed  pulley. 

118.  Movable  Pulley. — The  case   is   different   when  we 
have  a  pulley  such   as   is   shown   in  Fig.  41.     Here  the 
weight  is  supported  by  both  branches  of  the  cord  above 


54 


NATURAL   PHILOSOPHY. 


the  pulley,  hence  the  tension  on  each  need  be  but  half 


W 


Fio.  40.— FIXED  PULLEY. 


W 


FIG.  41. — MOVABLE  PULLEY. 


the  weight;  that  is,  for  equilibrium,  W  must  be  twice  P. 
A  pulley  of  this  kind  will,  therefore,  enable 
a  power  of  one  pound  to  lift  a  weight  of  two 
pounds.  Such  a  pulley  is  called  a  movable 
pulley. 

119.  Work  done. — Since,  when  W  is  lifted  any 
distance,  the  pulley  is  elevated  the  same  amount, 
the  ropes  at  both  a  and  b  will  be  shortened,  and  P 
will    have    to  rise   through   twice   this   distance. 
Hence,  as  in  the  lever,  in  order  to  gain  the  advan- 
tage of  the  movable  pulley,  we  lose  space  and  time. 
The  work  done  by  the  power  is  equal  to  the  work 
done  by  the  weight. 

120.  Combination    of    Pulleys.— In    the 

combination  of  pulleys  of  Fig.  42,  the  three 
upper  ones  are  fixed  pulleys,  and  only 
change  direction.  The  three  lower  are 
movable  pulleys,  and  each  doubles  the  ef- 
fective force  applied  to  it,  so  that  a  power 
can  lift  a  weight  six  times  its  own  weight. 
The  general  rule  for  pulleys  is  that  a  power 


w 


FIG.  42. — COMBINA 
JJON  OF  PULLEYS. 


MOTION  AND  FORCE. 


55 


can  lift  a  weight  as  many  times  greater  than  itself  as  twice 
the  number  of  movable  pulleys. 

How  would  this  rule  be  affected  if  the  rope  began  at  the  upper 
movable  pulley  ? 

Exercises. — 1.   In  Fig.  43,  how  much  weight  will  a  power  of  20 
pounds  lift  ? 

2.  If  the  power  moves  through  30  feet,  how  far  will  the  weight 
move  ? 

3.  How  much  power  will  be  required  to  lift  a  weight  of  1  kilogram 
through  1  metre,  and  through  what  distance  will  it  move  ? 


FIG.  43.— PULLETS. 


FIG.  44.— PULLEY  AND  WINDLASS. 


4.  In  a  system  of  pulleys,  a  power  of  2  pounds  balances  a  weight 
of  24  pounds :  how  many  movable  pulleys  are  employed  ? 

5.  In  the  combination  of  pulley  and  windlass  of  Fig.  44,  ab  is  2 
feet,  ac  6  inches.     A  power  of  30  pounds  is  applied  at  b :  how  much 
weight  can  be  lifted  ? 

6.  How  many  turns  will  be  required  to  lift  the  weight  through  3 
feet? 

THE   INCLINED  PLANE. 

121.  Law  of  the  Inclined  Plane. — Less  power  is  required 
to  roll  a  body  up  an  inclined  plane  than  F 

to  lift  it  through  the  height  of  the  plane. 
Hence  we  gain  by  its  use. 

Let  A  be  a  body  resting  on  an  inclined  "/^J  )o 

plane,  EF.     Let  the  weight  of  the  body  E 


be  represented  by  the  line  AB,  directly  FIG.  45.-iNCLiNED  PLANE. 

downward.   Let  this  be  resolved  into  two 

forces,  AC,  perpendicular  to  the  plane,  and  AD,  parallel 


56 


NATURAL  PHILOSOPHY. 


to  it.  Then  AC  makes  pressure  against  the  plane,  and  AD 
tends  to  make  the  body  roll  or  slide  down  ;  and  if  a  force 
parallel  to  EF,  and  equal  and  opposite  to  AD,  be  applied  to 
the  body,  it  will  be  in  equilibrium. 

By  geometry  we  readily  prove  the  proportion  that 

AD  :  AB  ::  FG  :  EF, 

or,  as  the  force  required  to  hold  the  body  on  the  plane,  which 
we  may  call  the  power,  is  to  the  weight  of  the  body,  so  is 
the  height  of  the  plane  to  its  length.    When  the  power  acts 
parallel  to  the  plane,  we  have  then  for  equilibrium, 
Power  :  Weight  : :  Height  of  Plane  :  Length, 
or,  the  weight  is  as  many  times  greater  than  the  power  as 
the  length  is  greater  than  the  height  of  the  plane. 

Exercises.— In  the  above  case,— 1.  Given  EF  =  10,  FG  =  5,  W~ 
200.     Find  P. 

2.  Given  EF  =  10,  FG  =  5,  P  =  40.     Find  W. 

3.  Given  EG  =  4,  FG  =  3,  W=  200.     Find  P. 


FIG.  46. — COMBINATION  OF  POWERS. 


4.  In  the  combination  of  lever,  inclined  plane,  and  pulley  of  Fig. 
46,  AB  =10  feet,  AC=2  feet,  DF  =  20  feet,  EF=8  feet,  P=100 
pounds  :  how  large  a  weight  can  be  lifted  ? 

5.  How  much  power  will  be  needed  to  lift  a  ton  ? 

6.  How  far  will  P  have  to  move  to  drag  W  through  1  foot  ? 

THE   WEDGE   AND  SCKEW. 

122.  The  Wedge. — If  the  inclined  plane  is  pushed  under 
the  body,  it  becomes  a  wedge,  and  the  same  rules  for  equi- 
librium hold  good.  The  height  of  the  plane  is  now  the 
back  of  the  wedge,  and  the  weight  is  as  many  times  greater 
than  the  power  as  the  length  exceeds  the  back  of  the  wedge. 

Wedges  are  used  for  splitting  timber,  for  raising  heavy 


MOTION  AND   FORCE. 


57 


weights,  for  cutting  and  piercing.     Knives,  scissors,  awls, 
chisels,  pins,  needles,  are  wedges. 

123.  The  Screw. — A  screw  is  an  inclined  plane  wound 
around  a  cylinder. 

Experiment  20. — Take  a  triangle  of 
paper,  as  in  Fig.  47,  and  wind  it  around  a 
round  piece  of  wood  ;  it  will  illustrate  how 
an  inclined  plane  can  be  made  into  ascrew.1 


FIG.  47.— SCREW  AND  IN- 
CLINED PLANE. 


124.  Law  of  the  Screw,— One  com- 
plete turn  of  the  screw  will  lift  the 
weight  through  the  distance  which 

separates  the  threads.  The  law  of  the  screw  is,  there- 
fore, that  the  weight  is  as 
many  times  greater  than  the 
power  as  the  circumference 
described  by  the  power  is 
greater  than  the  distance  be- 
tween the  threads. 

Exercise. — A  power  of  30 
pounds  applied  at  the  end  of  a 
lever  2  feet  long  acts  on  a  screw, 
the  distance  between  the  threads 
of  which  is  ^  of  an  inch :  how 
much  weight  can  be  lifted  ? 

In  the  common  screw,  propelled  by  a  screw-driver,  the 
weight  is  the  resistance  of  the  material  penetrated,  and  the 
circumference  described  by  the  power  is  the  circle  through 
which  the  largest  part  of  the  handle  travels.2 

125.  Friction. — All  the  laws  of  machines  are  modified 
by  friction.     Friction  is  roughness  at  the  point  of  contact 
of  two  surfaces,  which  prevents  them  from  sliding  freely 
on  each  other.     In  levers  there  is  friction  at  the  fulcrum, 
in  the  wheel  and  axle  and  pulley  at  the  bearings,  on  the 

1  Such  a  curve  is  a  helix,  and  not  a  spiral,  as  often  stated.    A  spiral 
is  a  curve  in  one  plane. 

2  The  distance  between  the  threads  of  a  fine  screw  is  best  obtained 
by  measuring  an  inch  along  it  and  counting  the  number  of  threads. 


FIG.  48. — THE  SCREW. 


58  NATURAL   PHILOSOPHY. 

inclined  plane,  wedge,  and  screw  at  their  surfaces.  In  all 
these  cases  this  represents  so  much  resistance,  to  overcome 
which  additional  power  is  required.  It  is  important  to  as- 
certain the  amount  of  friction  be- 
tween surfaces  of  different  kinds,  so 
that  its  effect  may  be  accurately 
taken  into  account  in  our  theories 
of  machines.  The  following  will 
afford  a  means  of  testing  its  amount. 

Experiment  21. — Fasten  a  pulley  to  the 
table,  as  in  Fig.  49.     Place  a  block  on  the 
FIG.  49.— DETERMINING  FRIG-     table  and  attach  the  pulley-cord  to  it.     On 
TION-  the  other  end  of  the  cord  apply  weights  till 

the  block  begins  to  move.     The  amount  of 

these  weights  will  measure  the  friction  between  the  block  and  the 
table. 

Experiment  22.— Place  a  brick  on  end,  then  on  face  on  the  table. 
The  friction  will  be  the  same  in  both  cases. 

Place  a  second  brick  on  top  of  the  first,  the  friction  will  be  doubled. 

126.  Laws  of  Friction. — By  some  such  arrangement  as 
this  it  has  been  found, — 

1.  That  friction  is  less  between  metals  of  different  kinds 
than  between  metals  of  the  same  kind.     Hence  the  advan- 
tage of  brass  bearings  for  iron  axles. 

2.  That  it  is  proportional  to  the  weight  (or  pressure), 
and  does  not  depend  on  extent  of  surface  in  contact. 

3.  That  it  is  greater  at  the  start  than  after  motion  has 
commenced.     A  part  of  the  weight  may  be  removed  from 
the  cord,  and  it  will  continue  to  descend.     The  object  of 
lubricants  is  to  diminish  friction. 

127.  Friction  Essential. — Friction  should  not  be  looked 
upon  as  a  resistance  merely  :  it  is  indispensable  to  our  wel- 
fare.    It  is  the  friction  between  our  feet  and  the  ground 
v/hich  saves  us  from  falling  at  every  step.    It  is  the  friction 
between  the  particles  of  dirt  and  the  rocks  which  prevents 
all  the  hills  from  crumbling  down  and  everything  being  re- 
duced to  a  dead  level.    It  is  the  friction  of  nails  and  screws 
which  gives  them  their  utility  and  .prevents  all  our  struc- 


MOTION  AND  FORCE.  59 

tures  from  falling  in  ruins.  It  enables  the  engine  to  draw 
us  on  the  track ;  it  gives  to  belted  wheels  their  value ;  it 
enables  long  ropes  to  be  made  out  of  short  strands,  and 
keeps  knots  tied ;  it  causes  the  rivers  to  flow  gently  along 
their  beds. 

128.  Machines  do  not  create  Energy. — We  have  seen  both 
in  the  lever  and  in  the  pulley  that  the  work  done  by  the 
power  is  equal  to  the  work  done  by  or  upon  the  weight  or 
resistance.     This  is  a  general  law  of  machines.     Whenever 
we  gain  power  we  lose  speed,  and  when  we  gain  speed  we 
lose  power.     A  machine   cannot  create  any  energy.     It 
transmits  that  which  is  applied  to  it  by  an  external  power. 
The  power  does  work  upon  it,  and  it  does  work  upon  the 
resistance.     This  work  may  be  of  a  different  kind,  but  is 
the  same  in  amount. 

129.  Uses  of  Machines. — The   question   then  comes  up, 
What  do  we  gain  by  machines  ?     Sometimes  we  gain  only 
a  change  of  direction,  as  in  the  fixed  pulley  ;  sometimes  it 
is  an  advantage  to  gain  power  at  the  expense  of  velocity, 
as  in  a  lever  or  pulley  used  to  raise  a  heavy  weight ;  and 
sometimes  it  is  an  advantage  to  gain  velocity  at  the  ex- 
pense of  power,  as  in  the  case  of  a  clock,  where  the  slow 
falling  of  the  weight,  or  uncoiling  of  the  spring,  may  cause 
rapid  motion  of  the  hands  ;  or  in  the  sewing-  or  mowing- 
machines.     Sometimes  it  is  a  gain  to  change  the  character 
of  the  power,  as  in  the  steam-engine,  where  heat  produces 
mechanical  motion,  or  in  electric  lighting-machines,  where 
heat  and  motion  produce  electricity  and  light.     Machines 
are  also  a  great  gain  in  enabling  us  to  use  the  power  of  the 
wind,  of  steam,  of  falling  water,  and  of  animals. 

130.  Perpetual  Motion. — These  examples  will  show  the 
character  of  the  gains  of  machinery.     In  no  case  is  the 
energy  increased  by  the  machine  itself.     We  see,  then,  the 
folly  of  all  perpetual-motion  machines, — machines  which  will 
keep  themselves  running  without  the  addition  of  any  ex- 
ternal energy.     Any  such  machine  would  have  to  create 


60  NATURAL  PHILOSOPHY. 

energy.  Let  us  suppose  that  water  falling  on  a  wheel 
would  cause  such  motion  of  the  wheel  as  would,  applied  to 
a  pump,  force  the  water  up  to  the  level  from  which  it  fell. 
This  would  be  a  perpetual-motion  machine,  for  it  would 
keep  itself  going  forever  without  any  new  supplies  of 
force.  But  it  requires  just  as  much  energy  to  lift  the 
water  up  to  its  level  as  is  given  out  by  the  fall.  But  part 
of  the  energy  of  the  fall  is  required  to  overcome  the  fric- 
tion of  the  machinery  and  the  resistance  of  the  air,  hence 
there  cannot  be  enough  left  to  raise  the  water  to  its  old 
level.  If  machines  could  be  constructed  so  as  to  run  with- 
out any  resistance,  perpetual  motion  would  be  possible,  and 
under  no  other  circumstances. 

Such  a  machine  would  be  useless  for  any  practical  pur- 
poses, for  if  any  machinery  were  connected  with  it,  it  would 
soon  bring  it  to  rest,  and  a  new  supply  of  power  would 
be  needed. 


General  Exercises.1 — 1.  The  minute-hand  of  a  watch  is  twice  as 
long  as  the  second-hand  :  show  that  the  end  of  the  second-hand  moves 
thirty  times  as  fast  as  the  end  of  the  minute-hand. 

2.  Find  the  space  described  in  the  fifth  second  by  a  falling  body. 

3.  If  a  body  falls  for  a  quarter  of  a  minute,  show  that  at  the  end  of 
that  time  it  would  be  moving  at  the  rate  of  483  feet  per  second,  and 
ascertain  what  this  velocity  will  be,  expressed  in  miles  per  hour. 

4.  A  stone  dropped  into  a  well  is  heard  to  strike  the  water  in  two 
seconds  and   a  half;    find   the  depth  of  the  well.     Ans.  100  feet. 

5.  An  express  train,  66  yards  long,  moving  at  the  rate  of  40  miles 
an  hour,  meets  a  slow  train,  110  yards  long,  moving  at  the  rate  of  20 
miles  an  hour  ;  find  how  long  a  man  in  the  express  train  takes  to 
pass  the  slow  train,  and  how  long  the  express  train  takes  in  completely 
passing  the  slow  train.     Ans.  -fa  minute,     •fa  minute. 

6.  A  river,  one  mile  broad,  is  running  downward  at  the  rate  of  4 
miles  an  hour ;  a  steamer  can  go  up  the  river  at  the  rate  of  6  miles 
per  hour ;  find  at  what  rate  it  can  go  down  the  river.     Ans.  14. 

7.  A  moving  body  is  observed  to  increase  its  velocity  by  a  velocity 
of  8  feet  per  second  in  every  second ;  find  how  far  the  body  would 
move  from  rest  in  5  seconds.     Ans.  100  feet. 

1  In  these  and  other  exercises  at  the  ends  of  the  chapters  a  great 
variety  is  given  in  quality  and  hardness.  The  teacher  should  make  a 
selection  adapted  to  the  class.  Many  classes  had  better  omit  all  of 
them,  while  some  would  be  benefited  by  working  them  all. 


MOTION  AND  FORCE.  61 


8.  A  body  is  moving  at  a  given  instant  with  a  velocity  of  40  feet 
per  second  ;  from  this  instant  a  constant  force  is  made  to  act  on  it  in 
a  direction  opposite  to  that  of  the  motion  which  brings  it  to  rest 
after  it  has  described  20  feet ;   find  the  proportion  which  this  force 
bears  to  the  weight  of  the  body.     Am.  About  1£  times. 

9.  A  man  jumps  suddenly  off  a  platform  with  a  20-pound  weight 
in  his  hand  :  find  the  pressure  of  the  weight  on  his  hand  while  he  is 
in  the  air. 

10.  Forces  represented  by  4,  5,  and  10  pounds  respectively  act  on  a 
particle  :  show  that  they  cannot  keep  it  at  rest. 

11.  A,  B,  C,  D  is  a  square.     A  force  of  4  pounds  acts  from  A  to 
B,  a  force  of  6  pounds  from  B  to  C,  and  a  force  of  10  pounds  from  C 
to  D  :  find  their  resultant.    Ans.  8:48. 

12.  It  is  required  to  substitute  for  a  given  vertical  force  two  others, 
one  horizontal  and  one  inclined  at  an  angle  of  45  degrees  to  the  ver- 
tical :  determine  by  a  diagram  the  magnitude  of  these  two  forces. 

13.  A  weight  of  24  pounds  is  suspended  by  two  strings,  one  of 
which  is  horizontal,  and  the  other  is  inclined  at  an  angle  of  45  de- 
grees to  the  vertical  direction  :  find  by  a  diagram  the  tension  of  each 
string. 

14.  A  straight  rod  is  bent  at  right  angles,  so  that  one  part  is  twice 
as  long  as  the  other  :  show  how  the  centre  of  gravity  of  the  bent  rod 
can  be  determined. 

15.  Show  that  a  cylinder,  if  placed  on  its  flat  end,  will  be  in  stable 
equilibrium,  but,  if  placed  on  its  curved  surface,  in  neutral  equilib- 
rium. 

16.  A  triangular  board  is  hung  by  a  string  attached  to  one  corner : 
find  what  point  in  the  opposite  side  will  be  in  a  line  with  the  string. 

17.  Find  where  the  fulcrum  must  be  placed  that  2  pounds  and  8 
pounds  may  balance  at  the  extremities  of  a  lever  5  feet  long. 

18.  The  arms  of  a  lever  are  respectively  15  and  16  inches  :  find 
what  weight  at  the  end  of  the  short  arm  will  balance  30  pounds  at 
the  end  of  the  long  arm,  and  what  weight  at  the  end  of  the  long  arm 
will  balance  30  pounds  at  the  end  of  the  short  arm. 

19.  A  straight  lever,  6  feet  long,  and  heavier  towards  one  end  than 
the  other,  is  found  to  balance  on  a  fulcrum  2  feet  from  the  heavier 
end,  but  when  placed  on  a  fulcrum  at  the  middle  it  requires  a  weight 
of  3  pounds  hung  at  the  lighter  end  to  keep  it  horizontal :  find  the 
weight  of  the  lever.     Ans.  9  Ibs. 

20.  Two  men,  A  and  B,  carry  a  weight  of  200  pounds  on  a  pole 
between  them ;  the  men  are  5  feet  apart,  and  the  weight  is  at  a  dis- 
tance of  2  feet  from  A  :  find  the  weight  which  each  man  has  to  bear. 

21.  Suppose  that  a  body  which  really  weighs  1  pound  appears  in 
a  balance  to  weigh  1  pound  1  ounce  :  find  the  proportion  of  the  length 
of  the  arms. 

22.  A  substance  is  weighed  from  both  arms  of  a  false  balance,  and 
its  apparent  weights  are  9  and  4  pounds  :  find  the  true  weight. 

23.  The  radius  of  the  axle  of  a  capstan  is  1  foot :  if  four  men  push 
each  with  a  force  of  100  pounds  on  spokes  5  feet  long,  show  that  on 
the  whole  a  tension  of  2000  pounds  can  be  produced  on  the  rope  which 
passes  around  the  axle. 

24.  A  wheel  and  axle  is  used  to  raise  a  bucket  from  a  well ;  the 

6 


62  NATURAL  PHILOSOPHY. 


circumference  of  the  wheel  is  60  inches,  and  while  the  wheel  makes 
three  revolutions  the  bucket,  which  weighs  30  pounds,  rises  one  foot : 
find  the  smallest  force  which  can  turn  the  wheel. 

25.  Suppose  the  power  to  act  parallel  to  the  plane,  and  that  the 
height  of  the  plane  is  to  its  base  as  5  is  to  12 :  if  the  weight  is  65 
pounds,  find  the  power. 

26.  Find  the  relation  between  the  power  and  the  weight  in  a  screw 
which  has  10  threads  to  an  inch,  and  is  moved  by  a  power  acting  at 
right  angles  to  an  arm  at  the  distance  of  1  foot  from  the  centre. 

27.  A  pendulum  vibrates  65  times  in  a  minute :  how  much  must  it 
be  lengthened  to  vibrate  once  in  a  second  ? 

Solution. —  Time  of  one  vibration  =  if  second. 

Hence,  from  formula  if  =  3.1416  V ' ^ 
(ilfOTe)2^    From  this  we  fi^d  !• 

In  a  seconds  pendulum  we  have  1  =  3.1416  Kgy      The  difference 
between  the  two  values  of  1  will  be  the  answer. 

28.  In  what  time  would  a  seconds  pendulum  vibrate  at  a  height  of 
4000  miles  above  the  earth's  surface  ?  at  a  depth  of  2000  miles  under 
ground  ? 

29.  How  long  is  a  pendulum  which  vibrates  40  times  a  minute  ? 

30.  A  seconds  pendulum,  carried  up  a  mountain,,  vibrates  58  times 
a  minute :  what  is  the  force  of  gravity  ? 


LIQUIDS.  63 


CHAPTEE  III. 

LIQUIDS. 
SECTION  I.— HYDROSTATICS, 

131.  Definitions. — In  Art.  25  we  were  taught  that  liquids 
are  substances  in  which  there  is  perfect  freedom  of  the 
molecules  among  themselves,  and  that  they  change  their 
form  with  the  slightest  force.     No  liquid  fulfils  these  con- 
ditions perfectly,  but  many  do  this  near  enough  for  all 
practical  purposes.     Water  is  commonly  used  as  the  typi- 
cal liquid,  and  will  be  so  used  here. 

Liquids  will  be  treated  under  two  heads, — liquids  at  rest 
and  liquids  in  motion.  Hydrostatics  is  the  science  which 
treats  of  liquids  at  rest. 

132.  Liquids  almost  Incompressible. — Liquids  can  scarcely 
be  compressed  even  if  subjected  to  the  greatest  pressure. 
Indeed,  it  was  formerly  thought  that  they  could  not  be 
compressed  at  all.     Many  years  ago  some  philosophers  in 
Florence  filled  a  hollow  silver  ball  with  water,  and,  after 
closing  the  opening,  squeezed  the  sides  together  by  great 
pressure.     This  pressed  the  ball  out  of  its  spherical  shape, 
and,  as  this  would  make  the  cavity  smaller,1  they  hoped  to 

1  It  is  proved  in  higher  mathematics  that  a  hollow  sphere  has  a 
greater  capacity  than  a  vessel  of  any  other  shape  which  is  enclosed 
hy  the  same  surface.  Hence,  when  the  shape  of  the  silver  vessel  was 
changed,  its  shell  would  not  hold  so  much  water ;  but,  as  indicated 
above,  instead  of  shrinking  to  fit  its  smaller  quarters,  the  water 
oozed  through  the  sides. 

Tyndall  calls  attention  to  the  fact  that  Bacon  performed  this  ex- 
periment fifty  years  before  it  was  performed  in  Florence ;  but  this 
fact  is  generally  unknown,  and  Bacon  seldom  gets  credit  for  it. 


64 


NATURAL   PHILOSOPHY. 


compress  the  water.  But,  instead  of  shrinking  in  bulk,  the 
water  came  through  the  thick  silver  sides,  and  spread  over 
the  outside  like  dew. 

But  by  using  better  apparatus  modern  experimenters 
have  been  able  to  compress  water  and  other  liquids  slightly. 
To  compress  a  quantity  of  water  whose  upper  surface  is  a 
foot  square  into  a  bulk  only  yi^-  less  would  require  a  pile 
of  iron  weights,  each  1  foot  square,  more  than  i  of  a  mile 
high.  For  all  practical  purposes,  therefore,  water  is  incom- 
pressible. This  property  of  liquids  will  be  illustrated 
presently  in  water  machinery,  and  is  of  great  use  to  us 
there. 

133.  Liquids  perfectly  Elastic. — If  liquids  are  compressed, 
and  even  if  kept  compressed  for  a  great  length  of  time, 
they  always  expand  to  their  original  bulk  when  the  press- 
ure is  removed.  Hence  we  infer  that  they  are  perfectly 
elastic. 

Experiment  23. — Throw  a  flat 
stone  very  slantingly  on  the  sur- 
face of  a  pond  of  still  water,  and 
notice  how  it  rebounds  or  "  skips" 
again  and  again.  What  causes 
it?  Does  a  stone  skip  so  well  on 
smooth  ice  ?  Why  not  ? 

134.  Liquids  transmit  Press- 
ure equally  in  all  Directions. 

— The  most  remarkable  and 
important  fact  about  liquids 
is  that  whenever  any  press- 
ure is  put  upon  one,  the  liquid 
presses  out  with  the  same  force 
in  every  direction. 

FIG.  50.— THE  PRESSURE  OF  LIQUIDS  THE 

SAME  IN  EVERY  DIRECTION.  In  Fig.  50,  the  piston  A  presses 

down  upon  one   square   inch   of 

water  with  a  force  of  1  pound.  This  force  is  transmitted  to  every  part 
of  the  surface,  and  the  liquid  therefore  presses  with  the  force  of  1  pound 
upon  each  square  inch  of  the  surface  of  the  vessel,  as  is  shown  by  its 
sustaining  the  weights  at  B,  C,  D,  and  E. 

To  which  class  does  the  lever  at  C  belong?    at  D  ?   at  E?    Has 


LIQUIDS. 


the  weight  of  the  water  been  taken  into  account  here  ?     "Would  it 
make  any  difference  ? 

135.  The  transmitted  Pressure  proportional  to  the  Sur- 
face  In  Fig.  51,  if  the  small  tube  is  1  inch  square  and 

the  large  one  4,  then  the  area 

of  the  water  pressing  on  the 
large  piston  is  16  times1  as  great 
as  upon  the  small  one,  and  with 
an  upward  pressure  of  1  pound 
upon  each  square  inch  of  B,«the 
whole  upward  pressure  then  is  16 
pounds.  This  is  called  the  hydro- 
static paradox,  because  it  seems 
paradoxical  (or  beyond  belief) 

that    1   pound    Should    balance    16        ^  FIG.  51.— THE  HYDROSTATIC 

pounds. 

136.  The  Hydrostatic  Press. — If  more  than  a  pound  be 
placed  upon  C  (Fig.  51),  the  piston  A  will  be  forced  down 
and  D  will  be  raised.     In  this  way  a  small  weight  can  be 
made  to  raise  a  very  large  one.     This  is  the  principle  of 
the  hydrostatic  press,  which  is  shown  in  Fig.  52.     In  order 
that  all  of  the  parts,  and  the  manner  of  working,  may  be 
seen,  the  figure  represents  the  press  cut  open  through  the 
middle,  or  in  section,  as  this  is  called.     The  raising  of  the 
piston  p  sucks  up  water  from  m.     When  the  handle  HE 
is  pushed  down  again,  a  valve  keeps  the  water  from  going 
back  into  m,  and  it  is  forced  through  the  narrow  tube  into 
M,  and  the  large  piston  P  is  raised  and  pressed  against  the 
cotton-bale  C  with  great  force.     If  p  is  1  inch  in  diameter, 
and  P  10  inches,  for  every  pound  down  upon  p  there  is  a 
pressure  of  100  pounds  upon  the  cotton-bale.    This  force  is 
usually  further  increased  by  using    a    lever,  GE  (which 
class  ?),  to  increase  the  pressure  upon  p. 

1  The  student  will  not  forget  that  the  areas  of  similar  surfaces  vary 
according  to  the  squares  of  their  like  dimensions. 
e  6* 


66 


NATURAL   PHILOSOPHY. 


137.  The  Hydrostatic  Press  creates  no  New  Force.— The 
hydrostatic  press  may  seem  to  contradict  Art.  130,  where 
it  is  said  that  power  is  never  created  by  machinery.  But 


FIG.  52.--THE  HYDROSTATIC  PRESS. 

the  surface  of  the  water  which  presses  up  against  P  is 
100  times  as  great  as  that  pressed  upon  by  p,  and  therefore 
when  the  small  piston  has  been  forced  down  1  foot  P  has 
been  raised  only  yj-g-  of  a  foot.  So  that  our  force  of  1  pound 
moving  through  1  foot  has  been  changed  to  a  force  100 
times  as  great,  but  moving  through  only  y^-  of  a  foot,  and 
therefore  exactly  equivalent  to  the  first  force. 

The  loss  of  power  by  friction  has  not  been  taken  into 
account  here,  and  less  power  is  lost  by  it  in  this  machine 
than  in  almost  any  other.1  On  this  account,  and  because 


1  About  10  per  cent,  of  the  power  is  usually  lost  by  friction.  The 
principle  of  the  hydrostatic  press  has  been  known  for  more  than  two 
hundred  years,  but  no  way  of  making  the  joints  tight  enough  to  resist 
the  enormous  pressure  of  the  water  was  found  until  Bramah,  an  Eng- 
lish inventor,  about  the  beginning  of  the  present  century,  invented  a 
curved  leather  collar  for  this  purpose,  shown  in  Fig.  52,  at  a  and  b. 


LiqviDS.  67 


by  enlarging  P  almost  any  power  can  be  accumulated  there, 
this  machine  is  in  common  use  where  great  force  is  needed. 
138.  Pressure  on  the  Bottom  of  a  Vessel,— In  a  vessel 
whose  bottom  is  level  and  sides  perpendicular,  the  pressure 
of  the  water  upon  the  bottom  is  evidently  equal  to  its 
weight,  as  in  Fig.  53,  A.  If,  now,  a  vessel  with  a  narrow 
stem,  but  widening  into  a  broad  base,  as  in  Fig.  53,  B,  be 
filled  with  water,  the  water  at  a,  being  pressed  upon  by 
the  weight  of  the  column  of  water  above  it,  transmits  this 
pressure  equally  in  every  direction  to  the  water  surround- 
ing it.  This  does  the  same  in  turn,  so  that  the  pressure  on 
every  part  of  the  bottom  of  the  vessel  is  the  same  as  on 
the  part  under  the  column.  Then,  in  Fig.  53  C,  the  press- 
ure at  E  is  equal  to  that  at  D,  and  therefore  the  pressure 
at  F  (or  at  H),  is  the  same  as  it  would  be  at  /  if  the  first 
joint  of  the  pipe  were  extended  straight  down  to  /.  And 
also  the  pressure  at  M  or  O  is  the  same  as  it  would  be  at 


FIG.  53. — PRESSURE  VARIES  WITH  THE  DEPTH. 

m.  If  the  tubes  were  curved,  or  had  any  other  shape,  the 
pressure  on  the  bottom  would  be  the  same.  Hence  the  fol- 
lowing important  principle :  In  a  vessel  of  any  shape  what- 
ever, the  pressure  of  a  liquid  upon  the  bottom  is  the  same  as 
if  the  sides  rose  perpendicularly  around  the  bottom,  and  it  were 
filled  with  the  liquid  to  the  same  height  as  at  present.1 

The  space  underneath  this  collar  is  connected  with  M,  so  that  the 
water  presses  the  collar  tighter  above  the  piston  as  the  pressure  in  M 
grows  greater,  and  prevents  the  water  from  leaking  there.    From  this 
discovery  the  hydrostatic  press  is  sometimes  called  Bramah's  press. 
1  The  bottom  of  the  vessel  is  understood  to  be  horizontal, — that  is, 


68 


NATURAL   PHILOSOPHY. 


A  cubic  foot  of  water  weighs  1000  ounces,  or  62 £  pounds.1 
Therefore,  to  find  the  pressure  of  water  on  the  bottom  of  a 
vessel,  find  the  number  of  cubic  feet  in  a  column  of  water 
whose  base  is  the  bottom2  of  the  vessel  and  whose  height 
is  the  perpendicular  height  of  the  surface  of  the  water  above 
the  base,  and  multiply  62J  pounds  by  this  number. 

139.  Pascal's  Experiment  with  the  Vases, — The  apparatus 


FIG.  54.— PASCAL'S  VASES. 

shown  in  Fig.  54  was  devised  by  Pascal3  to  prove  these  truths  ex- 
level.  For  the  pressure  upon  the  bottom  when  it  is  not  horizontal, 
see  Art.  140. 

1  More  exactly,  a  cubic  foot  of  pure,  fresh  water  at  32°  F.  (what 
does  that  mean?)  weighs  62£&o  pounds,  and  slightly  less  at  higher 
temperatures.     A  cubic  foot  of  sea-water  weighs  about  64J  pounds. 

2  Should  the  outside  or  the  inside  area  of  the  bottom  be  taken  ? 

3  Pascal  (Pascal)  was  born  in  France  in  1623,  and  died  there  in 


LIQUIDS.  69 


perimentally.  The  bottom  of  the  glass  tube  ca  is  loose,  and  hangs  by 
a  string  from  one  arm  of  a  balance.  Small  weights  are  put  on  the  othei 
arm  until  they  balance  the  bottom  and  the  string.  The  glass  tube 
be,  whose  sides  are  perpendicular,  is  screwed  on  at  c,  an  additional 
weight  of  1  pound  is  put  into  the  scale-pan  e,  and  water  is  poured  into 
be.  The  pound-weight  holds  the  bottom  close  against  the  end  of  the 
tube  until  a  pound  of  water  has  been  poured  in.  Then  the  water 
pushes  the  bottom  down,  and  runs  out  as  fast  as  more  is  poured  in, 
the  marker  d  having  been  set  so  as  to  show  the  height  of  the  water 
when  it  began  to  run  out. 

If,  now,  be  be  unscrewed  and  m  be  screwed  on  in  its  place,  it  will 
be  found  that  water  must  be  poured  in  to  exactly  the  same  height  as 
at  first  before  it  will  loosen  the  bottom  and  run  out,  although,  because 
of  the  widening  out  of  m,  there  may  be  2  pounds  of  water  in  it  then, 
thus  proving  that  the  pressure  on  the  bottom  depends  only  upon  the 
area  of  the  bottom  and  the  perpendicular  height  of  the  water.  If  n  be 
used,  perhaps  half  a  pound  of  water  will  fill  it  up  to  the  marker  d 
and  start  the  flow  of  water. 

140.  Pressure  on  the  Sides  of  a  Vessel, — Since  the  press- 
ure is  transmitted  equally  in  all  directions,  at  the  edge  of 
the  bottom  of  a  vessel  the  pressure  of  the  liquid  on  the 
side  is  the  same  as  on  the  bottom.  Half-way  up  to  the  sur- 
face it  is  the  same  as  the  downward  pressure  at  that  depth, 
or  half  as  great  as  at  the  bottom.  At  the  surface  there  is 
no  pressure  on  the  side.  Therefore  the  average  pressure 
per  square  inch  on  the  side  is  half  as  great  as  on  the  bot- 
tom. If,  then,  a  cubical  vessel  be  full  of  water,  the  pressure 
upon  each  of  the  four  sides  is  one-half  that  upon  the  base. 

In  the  above  case  the  sides  of  the  vessel  are  supposed  to  be  rect- 
angles, perpendicular  to  a  horizontal  base.  In  general,  the  average 
pressure  upon  the  perpendicular  sides  of  any  shape  is  the  pressure 
upon  the  centre  of  gravity  of  the  part  of  that  side  under  water. 

If  the  side  of  a  vessel  is  not  perpendicular,  the  pressure  upon  the 
part  of  the  side  under  water  is  the  same  as  if  that  part  were  laid  level 
and  covered  with  water  to  the  average  depth  of  the  water  upon  the 
inclined  side,  or  to  the  depth  of  the  centre  of  gravity  of  the  side. 

• 

1662.  He  was  a  very  brilliant  scientist,  who  did  much  for  Natural 
Philosophy,  especially  in  the  subject  we  are  now  considering.  He 
wrote  a  book  on  Conic  Sections  when  in  his  sixteenth  year. 


70 


NATURAL   PHILOSOPHY. 


A  vessel's  base,  which  is  not  horizontal,  may  be  considered  as  an 
inclined  side,  and  the  pressure  upon  it  found  in  the  same  way.  This 
is  a  different  thing  from  the  downward  pressure  in  such  a  vessel. 
That  is  the  same  as  the  weight  of  the  water,  and  would  be  found  by 
taking  a  horizontal  section  through  the  water  and  its  average  depth. 

141.  Pressure  on  the  Top  of  a  Vessel. — There  may  also  be 


05 1 


Intf.  55. — UPWARD  PRESSURE  OF 
LIQUIDS. 

an  upward  pressure  upon  the  top 
of  a  vessel.  Thus,  in  a  vessel 
shaped  as  in  Fig.  55,  the  pressure 
upward  at  H  or  F  is  just  the  same 
as  the  pressure  downward  at  B. 

Students  sometimes  cannot  see  how 
the  pressure  upon  the  bottom  DCE  can 
be  as  great  as  if  the  sides  went  up  to  a 
and  6,  and  yet  when  put  upon  scales 
and  weighed  the  whole  will  not  weigh 
nearly  so  much  as  the  other  vessel  of 
water  would.  It  is  because  the  press- 
ure upward  at  F  and  H  counterbalances 
a  part  of  the  pressure  downward  at  D 
and  E.  A  foot-ball  might  be  blown  so 
full  that  the  air  would  press  outward 
against  the  cover  with  a  force  of  sev- 
eral pounds  to  the  square  inch,  and  yet 

ordinary  scales  would  not  show  it  to  be  any  heavier  than  when  empty. 
The  pressure  within  is  as  great  up  as  down,  and  so  does  not  add  to 
the  weight. 

142.  The  Hydrostatic  Bellows. — Fig.  56  shows  a  common 
piece  of  apparatus  which  well  illustrates  these  principles. 


FIG.  56.— THE  HYDROSTATIC  BEL- 


LIQUIDS.  71 


The  narrow  tube,  about  six  feet  long,  is  screwed  into  the 
bellows,  and  water  poured  into  the  tube  will  raise  a  heavy 
weight  on  the  bellows.  When  the  bellows  are  distended, 
an  additional  pound  of  water  may  easily  sustain  100  pounds 
more  on  the  bellows. 

Few  persons  appreciate  the  amount  of  pressure  caused  by  a  con- 
siderable depth  of  water.  Pascal  long  ago  showed  that  a  strong  cask 
could  be  burst  by  screwing  into  it  a  long  tube  and  filling  cask  and 
tube  with  water.  Tanks  and  cisterns  would  be  much  less  likely  to 
leak  if  made  wide  and  shallow,  than  if  made  narrow  and  deep.  The 
pressure  in  the  water-pipes  of  cities  and  towns  is  often  very  great. 

Exercises. — 1.  Why  are  canal-banks  and  dam-breasts  made  thicker 
below  than  above  ? 

2.  If  water  be  thrown  hard  against  a  wall,  will  it  trickle  down  the 
wall,  or  fly  off?  Why? 

3.  If  in  the  vessel  shown  in  Fig.  51  one  side  of  A  is  2  inches  and 
one  side  of  B  12  inches,  and  if  5  pounds  were  put  upon  C,  what 
weight  upon  D  would  it  balance  ?     Ans.  180  pounds. 

4.  What  weight  must  be  put  upon  C  to  balance  396  pounds  upon  D  ? 

5.  If  you  should  stand  upon  C,  what  weight  upon  D  would  you 
balance  ? 

6.  If  you  should  stand  upon  D,  what  weight  upon  C  would  balance 
you  ? 

7.  What  weight  must  be  put  upon  C  to  make  B  stand  1  foot  higher 
than  A?     Ans.  l$f  pounds. 

8.  What,  if  B  were  6  inches  square?     Ans.   l^f  pounds. 

9.  What,  if  B  were  1  foot  square  and  A  6  inches  square  ?  Ans.  15f 
pounds. 

10.  In  a  hydrostatic  press  the  diameter  of  the  small  piston  is  1 
inch  and  that  of  the  large  piston  12  inches  :  how  great  a  weight  will 
be  raised  by  a  downward  pressure  of  50  pounds  upon  the  small  piston  ? 
Ans.  7200  pounds. 

11.  If  GE  (Fig.  52)  is  3  feet  and  GH  6  inches,  what  weight  will  be 
balanced  by  50  pounds  at  the  end  of  the  handle  ?   Ans.  43,200  pounds. 

12.  If  friction  were  taken  into  account,  how  much  would  these  be 
reduced  to  ?  * 

13.  If  a  tight  cover  were  put  upon  B  (Fig.  53),  and  it  were  turned 
upside  down,  would  the  pressure  of  the  water  upon  the  new  base  be 
the  same  as  upon  the  old  one  ? 

14.  Would  the  pressure  per  square  inch  be  the  same  ? 

15.  Would  it  weigh  the  same  in  a  pair  of  scales  ? 

?.6.  There  are  2150.4  cubic  inches  in  a  bushel :  what  weight  of  water 
would  fill  a  peck  measure?  Ans.  19$  pounds. 

17.  If  the  room  in  which  you  recite  these  lessons  were  filled  with 
water,  what  would  it  weigh  ? 

18.  A  cubical  vessel  is  full  of  water  :  how  many  times  its  weight 
is  the  pressure  of  the  water  upon  the  sides  and  bottom  together? 
Ans.  3  times. 


72  NATURAL  PHILOSOPHY. 

19.  A  vessel  of  water  is  2  feet  deep :  find  the  pressure  upon  each 
square  inch  of  the  bottom. 

20.  Upon  a  square  inch  of  the  side,  6  inches  above  the  bottom. 
Ans.  £f  f  pound. 

21.  Upon  a  square  inch  of  the  side,  18  inches  above  the  bottom. 

22.  In  Fig.  55,  if  AB  is  18  inches,  what  is  the  upward  pressure 
per  square  inch  at  F?     Ans,  i|f  pound. 

23.  If  a  hydrostatic  bellows  be  15  inches  square,  and  the  tube  be  6 
feet  long,  when  full  of  water  how  much  weight  will  the  bellows  sus- 
tain ?     Ans.  585^|  pounds. 

143.  Liquids  rise  to  a  Level. — In  communicating  vessels 
or  tubes,  liquids  rise  to  stand  at  a  level.     The  water-works 
of  a  town  illustrate  this  on  a  great  scale.   The  water,  seek- 
ing the  level  of  the  reservoir,  rises  from  the  underground 
pipes  up  into  the  highest  stories  of  the  houses. 

An  apparatus  consisting  of  a  vase,  connected  with  various  crooked 
glass  tubes,  is  often  used  to  illustrate  this,  but  a  common  coffee-pot 
is  about  as  good.  The  coffee  stands  at  the  same  height  in  the  spout 
as  in  the  coffee-pot  itself. 

144.  Fountains,  Springs,  and  Wells.— It  is  water  seeking 
its  level  that  causes  fountains  and  artesian  wells.     But  in 


FIG.  57. — A  FOUNTAIN. 


a  fountain  the  stream  never  rises  quite  so  high  as  the  level 
of  the  reservoir,  on  account  of  friction  in  the  pipe,  resist- 
ance of  the  air,  and  the  interference  of  the  falling  drops 
with  the  upward  stream. 


LIQUIDS.  73 


When  rain  falls,  it  sinks  down  into  the  earth  until  it 
comes  to  a  layer  of  rocks  or  clay,  and  flows  along  this  to 
an  outlet,  generally  where  the  surface  of  the  ground  sinks 
down  to  the  level  of  the  bed  of  clay  or  rock.  This  is  a 
spring.  Where  there  is  no  spring,  a  pit  is  often  dug  down 
until  it  reaches  one  of  these  small  underground  streams, 
and  we  have  a  well. 

Artesian  wells  are  small  holes  only  a  few  inches  in  diameter,  bored 
into  the  earth  with  a  sort  of  auger.  They  are  often  many  hundreds 
of  feet  deep,  and  the  water  rises  in  them,  sometimes  flowing  out  at 
the  surface.  This  is  because  the  well  has  tapped  an  underground 
stream  of  water  which  has  flowed  down  there  from  high  ground. 
Fig.  58  makes  this  clear. 


FIG.  58. — AN  ARTESIAN  WELL. 

The  water  has  flowed  from  a  under  a  stratum  of  clay  or  rock,  be, 
through  which  the  water  cannot  rise  anywhere  until  the  well  is 
reached.  These  wells  have  been  sunk  in  all  parts  of  the  world,  and 
from  some  of  them  immense  quantities  of  water  flow.1  Many  of  the 
oil-wells  in  Pennsylvania  and  elsewhere  are  artesian  wells. 

1  These  are  called  artesian  because  the  first  one  was  at  Artois  (Ar- 
twa/)  in  France. 

At  Passy  (Pas-see'),  near  Paris,  there  is  an  artesian  well  1923  feet 
deep,  which  discharges  5,660,000  gallons  of  water  daily. 
D  7 


74 


NATURAL   PHILOSOPHY. 


145.  Water-Level. — The  surface  of  a  small  portion  of 
water  appears  to  be  perfectly  level,  and  is  practically  so, 
but  large  surfaces  of  water  are  found  to  be  perceptibly 
convex.1  This  necessarily  follows  from  the  fact  that  the 
earth  is  round,  the  water  taking  the  shape  of  the  earth. 


FIG.  59.— DEVIATION  OF  WATER-LEVEL  FROM  EXACT  LEVEL. 

The  surface  of  water  or  level  ground  falls  from  a  horizontal  line 

8  inches  at  the  end  of  one 
mile,  but  8  inches  multi- 
plied by  the  square  of  2  at 
the  end  of  two  miles,  and 
by  the  square  of  3  at  the 
end  of  three  miles,  etc. 

Why  are  not  the  plumb- 
lines  parallel  in  Fig.  59? 

146.  Spirit-Level.— 
This  very  common  in- 
strument is  a  glass 
tube  almost  filled  with  alcohol,  but  with  a  small  air-bubble 
left  in  it,  and  then  sealed  up  air-tight.  The  tube  looks  to 
be  perfectly  straight,  as  in  Fig.  60,  but  it  is  really  slightly 


FIG.  60.— A  SPIRIT-LEVEL. 


1  Do  not  forget  to  know  clearly  what  concave  and  convex  mean. 
You  can  remember  that  a  concave  surface  is  hollowed  out  like  a  cave, 
and  that  a  convex  one  has  just  the  opposite  shape. 


LIQUIDS.  75 


curved,  as  shown  (but  exaggerated)  in  Fig.  61.  When  the 
ends  of  the  tube  are  level,  the  middle  is  the  highest  point, 
and  the  light  bubble  is  found  there.  The  spirit-level  is 
constantly  used  by  carpenters  and  other  mechanics,  and  is 


B 

»- — 

A 

FIG.  61.— THE  CURVE  OF  A  SPIRIT-LEVEL  (EXAGGERATED). 

often  attached  to  telescopes,  and  to  surveying  and  other 
instruments. 

Alcohol  never  freezes  at  natural  temperatures,  and  is  therefore  the 
best  liquid  for  filling  levels. 

147.  Bodies  in  Water :  three  Important  Laws. 

Experiment  24. — Make  a  cube  of  wood1  5  centimetres  (2  inches) 
on  each  side,  weigh  it,  then  let  it  float  upon  a  vessel  which  was  full  of 
water.  Weigh  the  water  which  ran  over,  and  it  will  be  found  to  be 
the  same  as  the  weight  of  the  cube.  Therefore, 

I.  A  body  floating  in  water  displaces  its  own  weight  of  the 
water. 

"When  will  the  vessel  weigh  more,  full  of  water,  or  with  the  wood 
floating  in  it?  Try  it. 

Experiment  25. — Drive  enough  brads  or  tacks  without  heads  en- 
tirely into  the  wood  to  sink  it  in  water.  Drop  the  cube  into  a  ves- 
sel full  of  water.  Catch  the  water  which  runs  over  in  some  vessel  in 
which  you  can  measure  its  volume.  It  will  be  found  to  be  exactly 
125  cubic  centimetres  (8  cubic  inches).  Therefore, 

II.  A  body  immersed  in  water  displaces  its  own  bulk  of  the 

water. 

Could  this  principle  be  used  to  find  the  volume  of  an  irregular 
solid,  such  as  a  bunch  of  keys  or  a  watch-chain  ?  Could  you  do  it 
without  making  the  water  overflow  ? 

Experiment  26. — Hold  a  stone  by  a  string  in  the  air,  and  after- 
wards in  water  ;  notice  how  much  lighter  it  is  in  the  water ;  or,  more 
exactly,  hang  the  weighted  wooden  cube  by  a  thread  to  one  arm  of  a 

1  Any  piece  of  wood  will  do  equally  well  for  this  experiment,  but 
this  cube  will  be  most  convenient  for  the  succeeding  ones,  hence  the 
recommendation.  In  order  to  make  the  experiment  entirely  satis- 
factory, the  wood  ought  to  be  coated  with  varnish,  oil,  paraffin,  or 
something  of  the  sort,  to  keep  it  from  absorbing  water. 


76 


NATURAL   PHILOSOPHY. 


balance  and  weigh  it.  Then  let  it  hang  immersed  in  water  and  weigh 
it  again.  Its  weight  will  be  125  grams  (4J|  ounces),  the  weight  of  a 
cube  of  water  5  centimetres,  or  2  inches,  on  each  side.  Therefore, 

III".  A  body  immersed  in  water  is  lightened  by  the  weight  of 
its  bulk  of  water. 

Let  ABDC  represent  a  solid  block 
immersed  in  water.  It  is  pressed 
upward  at  CD  with  a  pressure  equal 
to  the  weight  of  the  column  of  water 
NCDN,  and  downward  at  AB  by  only 
the  weight  of  NABN ;  therefore  on 
the  whole  the  block  is  pressed  up- 
FlG-62-  ward,  or  lightened,  by  the  weight  of 

the  difference  of  these  two  columns,  or  ABDC. 


FIQ.  63.— THE  CYLINDER  AND  BUCKET  EXPERIMENT. 

Fig.  63  shows  a  piece  of  apparatus  which  illustrates  this  beautifully. 

The  cylinder  p  is  of  solid  metal,  and  fits  into  the  bucket  c  exactly. 
The  two  are  weighed  at  first  with  no  water  in  the  jar.  Water  is  then 
poured  into  the  jar  to  cover  p,  when  it  will  be  lightened,  and  the 
scale-pan  P  with  the  weights  will  fall.  But  if  c  be  filled  with  water, 
the  scales  will  balance  again.  Explain  this. 

148.  Floating  Bodies. — We  see,  then,  that  a  body  lighter 
than  water  floats  because  a  part  of  it  displaces  enough 


LIQUIDS. 


77 


water  to  equal  in  weight  the  whole  of  the  body.  Material 
much  heavier  than  water  can  be  floated,  if  it  is  thin  and 
hollowed  out  enough.  A  saucer  or  tin  basin  wrill  float, 
although  china  and  tin  are  heavier  than  water,  because 
to  sink  it  would  have  to  displace  a  bulk  of  water  equal  to 
the  shell  and  inside  together,  and  this  would  be  heavier 
than  the  shell  of  china  or  tin.  It  is  on  this  principle  that 
almost  all  large  ships  are  now  made  of  iron,  and  they  not 
only  float,  but  carry  immense  loads  of  freight. 

In  mechanics  (Art.  93)  we  learfied  that  a  body  stands 
most  stable  when  its  centre  of  gravity  is  lowest ;  and  the 
same  is  true  with  a  floating  body.  The  keels  of  ships  are 
often  heavily  weighted  with  metal ;  the  heaviest  part  of  the 
cargo  is  put  in  the  bottom  of  the  ship.  And  a  ship  never 
goes  to  sea  empty ;  if  no  cargo  can  be  got,  it  is  loaded  with 
stones  for  ballast. 

"Why  is  a  row-boat  much  more  apt  to  upset  when  you  stand  up 
than  when  you  sit  down  in  it  ? 

The  heavier  a  liquid,  the  better  will  a  body  float  in  it. 
Iron,  and  even  lead,  will  float  upon  mercury,  just  as  wood 


lillllllllllllllllllllllllllillllllllilllllillllillllllllll 

Fia.  64. — EGG  FLOATING  IN  BRINE. 

floats  upon  water.     Sea-water  is  heavier  than  fresh  water, 
so  that  a  vessel  sinks  lower  when  it  comes  into  a  fresh- 


78  NATURAL  PHILOSOPHY. 

water  river  from  the  ocean.      And  in  the  intensely  salt 
water  of  the  Dead  Sea  a  man  cannot  sink  if  he  wants  to. 

Experiment  27. — Fill  ajar,  such  as  is  shown  in  Fig.  64,  half  full 
of  fresh  water,  an  egg  will  sink  to  the  bottom  :  why  ? 

Fill  a  second  jar  half  full  of  strong  brine,  the  egg  will  float :  why  ? 

Pour  the  fresh  water  carefully  upon  the  brine,  and  the  egg  will 
sink  about  half-way  and  float  there  :  why  ?  Would  it  do  to  pour 
the  salt  water  in  upon  the  fresh  ?  Try  it. 

SPECIFIC   GRAVITY. 

149.  Definitions. — The  specific  gravity  of  a  solid  or  a  liquid 
is  its  weight  divided  by  the  'weight  of  an  equal  bulk  of  water. 

A  cubic  inch  of  iron  weighs  4.06  ounces,  and  a  cubic  inch  of  water 
.58  ounce".  The  specific  gravity  of  the  iron  is  4.06  -=-.58,  or  7.  A  cubic 
inch  of  alcohol  weighs  .522  ounce  :  what  is  its  specific  gravity? 

Pure  water  at  39°  F.,  the  temperature  at  which  it  is  densest,  is  the 
exact  standard  of  specific  gravity  for  solids  and  liquids. 

The  specific  gravity  of  a  gas  is  its  weight  divided  by  the 
weight  of  an  equal  bulk  of  air,  or  hydrogen,  at  a  temperature 
of  32°  F. 

To  find  the  Specific  Gravity  of  a  Solid. 

Experiment  28. — Hang  a  thick  screw  or  other  small  piece  of  iron 
from  one  scale  of  a  delicate  balance  by  a  fine  thread  ;  weigh  it  care- 
fully :  suppose  its  weight  is  found  to  be  350  grains.  Set  a  glass  of  water 
under  it,  and  let  the  screw  hang  in  the  water  ;  weigh  it  there :  suppose 
its  weight  is  300  grains.  According  to  Art.  147,  350  grains,  less  300 
grains,  or  50  grains,  is  the  weight  of  an  equal  bulk  of  water,  and,  there- 
fore, 350  grains  -r-  50  grains,  or  7,  is  the  specific  gravity  of  the  screw. 

Hence  the  specific  gravity  of  a  solid  heavier  than  water  can 
be  found  by  dividing  its  weight  by  its  loss  of  weight  when 
weighed  in  water. 

150.  To  find  the  Specific  Gravity  of  a  Solid  lighter  than 
Water. 

Experiment  29. — Take  a  small  cork,  weighing,  perhaps,  10  grains. 
Fasten  it  to  the  screw  used  before,  and  weigh  the  two.  They  will 
weigh  360  grains.  Weigh  them  in  the  water.  They  will  weigh  less 
than  the  screw  weighed  in  the  water,  perhaps  270  grains.  The  cork 
loses  all  of  its  own  weight  (10  grains)  and  buoys  up  30  grains  of  the 
weight  of  the  screw.  Hence,  according  to  Art.  147,  the  weight  of  the 
water  equal  to  the  cork  in  bulk  is  40  grains.  And  the  specific  gravity 
of  the  cork  is  10  grains  -r-  40  grains,  or  ^. 

Hence  the  specific  gravity  of  a  solid  lighter  than  water  can 


LIQUIDS. 


79 


be  found  by  dividing  its  weight  by  its  weight  added  to  what  it 
buoys  up  a  heavy  solid  previously  weighed  in  water. 

151.  The  Specific  Gravity  of  Liquids. — The  specific  gravity 
of  a  liquid  can  be  found  by  dividing  the  weight  of  a  quantity 
of  the  liquid  by  the  weight  of  an  equal  quantity  of  water.   Try 
it  with  strong  brine,  with  coal-oil. 

Specific  gravity  flasks  which  will  hold  a  certain  known  weight  of 
pure  water  at  39°,  say  1000  grains,  are  often  used  to  find  the  specific 
gravity  of  liquids.  The  flask  is  filled  with  the  liquid  whose  specific 
gravity  is  to  be  found,  and  weighed.  The  weight  of  the  empty  flask 
being  subtracted,  the  remainder  is  the  weight  of  the  liquid,  and  this 
divided  by  1000  grains  gives  the  specific  gravity  of  the  liquid. 

Experiment  30. — Take  a  heavy  solid,  say  the  screw  used  in  Exper- 
iment 28,  and  weigh  it,  then  weigh  it  in  water  :  suppose  the  weights  to 
be  350  and  270  grains  as  before.  Weigh 
it  also  in  strong  brine :  suppose  its 
weight  then  is  found  to  be  256  grains. 
From  its  losses  of  weight  in  the  water 
and  brine  can  you  find  the  specific 
gravity  of  the  brine  ?  How  does  the 
result  compare  with  the  specific  grav- 
ity which  you  found  for  the  brine  be- 
fore? Test  coal-oil  again  in  this  way. 

152.  Hydrometers. — Experiment 

31. — Get  a  piece  of  light  wood  about  a 
foot  long,  and  an  inch  square  all  the 
way  along.  Mark  the  inches  and 
quarters  of  inches  on  one  side.  Bore 
a  half-inch  hole  in  one  end,  and  pour 
it  full;  of  melted  lead.  Smooth  the 
end  off  with  knife  or  file,  and  varnish 
or  oil  the  stick  so  that  it  will  not  ab- 
sorb water.  You  have  made  a  hy- 
drometer.1 Put  it  in  water,  and  it  will 
stand  upright,  sinking  to  a  certain 
point.  It  will  be  convenient  to  make 
it  sink  to  some  inch-mark  by  cutting 
a  little  off  one  end.  (If  the  water- 
mark is  at  first  a  little  above  an  inch- 
mark,  which  end  will  you  cut  off? 

If  below,  which  one  ?  Why  ?)  Suppose  it  sinks  in  water  to  the 
8-inch  mark.  Put  it  in  the  brine.  It  will  stand  at  6|  inches.  (Why 
should  it  rise  higher  in  the  brine  than  in  water  ?  Do  not  be  satisfied 


FIG.  65.— HYDBOMETER. 


1  Hydrom'eter,  from  Greek  hudor,  water,  and  metron,  measure. 


80 


NATURAL  PHILOSOPHY. 


until  you  can  give  the  reason  clearly.^  Then  6|  cubic  inches  of  the 
brine  must  weigh  as  much  as  8  cubic  inches  of  water,  or  1  cubic  inch 
of  brine  1.2  times  as  much  as  1  cubic  inch  of  water,  and  the  specific 
gravity  of  the  brine  is  1.2.  With  this  hydrometer  the  specific  grav- 
ities of  other  liquids  can  be  quite  accurately  found.  Try  it  with 
coal-oil  or  other  oils,  milk,  or  any  other  convenient  liquid.  Glass 
hydrometers,  as  represented  in  Fig.  65,  are  in  common  use.  They 
are  commonly  weighted  with  mercury.  Special  instruments  of  this 
sort  are  often  used  to  test  milk,  alcohol,  acids,  etc. 

153.  Specific  Gravity  of  Gases. — The  specific  gravity  of 
a  gas  can  be  found  by  weighing  equal  quantities  of  it  and 
of  air,  and  dividing  the  first  by  the  second. 

154.  Capillary  Attraction. — We  learned  in  Art.  143  that 

liquids  seek  a  level ;  but  there  is  a  very 
curious  exception  to  this  law.     If  we 
notice  the  edge  of  the  water  in  a  glass 
vessel,  we  see  that  it  rises  up  in  a  curve. 
If  there  is  a  corner  in  the  vessel  (as  in 
a  square  inkstand),  it  rises  higher  there. 
If  two  glass  plates  are  held  in  water 
Parallel  and  close  together,  the  water 
will  be  higher  between  them  than  out- 
side ;  and  if  the  plates  be  brought  together  at  one  end,  the 
water  will  rise  higher  towards  this   end  in  a  peculiarly 
shaped  curve,1  as  in  Fig.  66.     But  if  the 
end  of  a  very  small  glass  tube  be  put  into 
water,  it  will  rise  in  it  best  of  all.     It  is 
from  this  fact  that  this  phenomenon  takes 
its   name  of  capillary  attraction,  from  a 
Latin   word   (capil'lus)    meaning   a   hair. 

FIG.  67.— CAPILLARY  AT- 

TRACTION  IN  TUBES.    Its  cause  has  DQQii  given  in  Art.  28. 

Experiment  32. — Color  some  water  with  a  small  quantity  of  indigo. 
Put  the  end  of  a  fine  glass  tube  (a  broken  thermometer  tube  will  be 
good)  into  it,  and  the  water  will  rise.  If  you  have  another  finer 
tube,  the  water  will  rise  higher  in  it.  And  if  you  have  the  simple 


1  It  is  proved  by  higher  mathematics  that  this  curve  is  an  hyperbola, 
— a  curve  very  familiar  to  mathematicians,  and  treated  of  in  Analyt- 
ical Geometry. 


LIQUIDS. 


81 


piece  of  apparatus  shown  in  Fig.  67,  you  will  notice  that  the  water 
rises  higher  and  higher  as  the  tubes  grow  finer.  And  careful  experi- 
ment shows  that  in  fine  tubes  the  height  to  which  a  liquid  will  rise  is 
just  in  proportion  to  the  fineness  of  the  bore. 

It  is  capillary  attraction  that  causes  a  sponge  to  absorb 
water,  a  blotter  to  absorb  ink,  a  lamp-wick  to  draw  up  oil, 
a  towel  to  dry  your  face  and  hands  when  they  are  wet. 
If  a  lamp-wick  or  rag  have  one  end  in  a  basin  of  water 
and  the  other  hanging  over  the  side  of  the  basin,  it  will 
slowly  drain  all  the  water  out  of  the  basin ;  but  any  im- 
purity in  the  water  will  remain  in  the  basin. 

155.  Capillary  Repulsion. — In  all  the  cases  of  capillary 


FIG.  68. — NEEDLES  FLOATING  ON  WATER. 


FIG.  09. — CROSS-SECTION  OF  A  FLOATING 
NEEDLE. 


attraction  mentioned  above,  it  will  be  found  that  the  water 
wet  the  substance  that  drew  it  up.     And  whenever  there 
is  capillary  attraction, 
it  will  be  .found  that 
the    liquid    wets    the 
solid.     But  if  a  glass 
plate  be  greased  or 
waxed    and    dipped 

into   Water,    the    SUr-  FIG.  70.— INSECT  WALKINO  ON  WATEB. 

face  water  around  it 

will  be  pushed  away.  And  if  the  inner  surface  of  a  capil- 
lary tube  be  oiled,  water  will  sink  in  it  below  the  level  of 
the  water  around  it.  You  will  notice  that  the  water  does 
not  wet  the  glass ;  and  whenever  a  liquid  will  not  wet  a  solid, 
f 


82  NATURAL   PHILOSOPHY. 

there  is  capillary  repulsion.     This  is  very  well  shown  with 
glass  tubes  and  mercury. 

If  a  fine  needle  be  greased  (which  can  generally  be  done  simply  by 
drawing  it  between  the  thumb  and  finger),  and  laid  carefully  upon 
the  surface  of  water,  it  will  float.  Fig.  68,  which  shows  a  cross-section 
of  the  needle  floating  upon  water,  explains  this.  The  water  will  not 
wet  the  greased  needle,  but  is  repulsed  from  it,  forming  a  trough 
around  the  needle.  And  the  needle  really  displaces  as  much  water  as 
would  fill  the  trough,  which  would  weigh  as  much  as  the  needle,  or  it 
displaces  its  own  weight  of  water.  In  the  same  way  we  can  explain 
how  certain  insects  walk  upon  the  surface  of  water. 

Exercises. — 1.  Why  do  doors  and  window-frames  swell  in  damp 
weather  ? 

2.  Why  does  water  keep  wooden  buckets  and  tubs  from  falling 
apart  ? 

3.  In  Fig.  51,  B  is  9  inches  square,  A  4  inches  square.    There  are  4 
pounds  upon  A,  and  it  is  level  with  B :    what  weight  is  upon  J5? 
Ans.  20^  pounds.     How  much  additional  weight  upon  B  will  make 
it  stand  8  inches  lower  than  A  ?    Ans.  23  pounds  7  ounces.     If,  when 
they  are  at  the  same  height,  8  pounds  be  put  upon  -4,  how  high  will 
B  stand  above  A  ?     Ans.  13£ff  inches. 

4.  If  B  is  15  centimetres  square,  and  A  is  6  centimetres  square, 
with  24  kilograms  upon  B,  what  must  be  upon  A  to  balance  it  ?   How 
much  additional  weight  upon  A  will  make  it  stand  12  centimetres 
lower  than  J5?    If,  when  they  are  at  the  same  height,  6  kilograms  be 
put  upon  B,  how  far  will  it  stand  below  A  ? 

5.  A  dam-breast  is  1000  metres  long,  it  slopes  from  the  surface  of 
the  water  to  a  depth  of  12  metres,  and  the  breadth  of  the  part  under 
water,  measured  slopingly,  is  15  metres  :  what  weight  of  water  in  kilo- 
grams rests  upon  the  breast  ?    Ans.  54,000  cubic  metres  =  54,000,000 
kilograms. 

6.  A  box  4  feet  long,  2  feet  wide,  and  3  feet  high  is  full  of  water : 
what  is  its  weight?     What  is  the  pressure  per  square  inch  upon  its 
bottom  ?   Ans.  Iff  pounds.    What  at  the  bottom  of  one  side  ?    What 
half-way  up  one  side  ?     Ans.  |~|f  pounds.     Half-way  up  one  end  ? 
Ans.  4||  pounds. 

7.  Suppose  a  piece  of  sheet-iron,  2  feet  wide,  is  run  from  the  lower 
part  of  one  end  to  the  top  of  the  other,  in  the  box  described  in  the 
last  problem  :  what  is  the  downward  pressure  upon  the  sheet-iron  ?  the 
upward  pressure  ?  What  is  the  downward  pressure  upon  each  square 
inch  of  the  sheet-iron  ?     Ans.  ||  pound. 

8.  When  a  hose  is  attached  to  a  hydrant,  why  will  it  not  throw  a 
stream  of  water  as  high  as  the  town  reservoir  ?     If  the  end  of  the 
hose  is  carried  high  enough,  will  the  water  rise  in  the  hose  as  high  as 
the  reservoir  ? 

9.  Why  are  springs  generally  on  hill-sides  or  in  low  places  ? 

10.  How  many  metres  must  a  man's  eye  be  from  the  ground  to  see 
5  kilometres  over  water  ?  to  see  100  kilometres?     Ana.  196-J-,  784.63. 


LIQUIDS. 


11.  How  far  out  at  sea  could  a  light-house  200  feet  high  be  seen  ? 
Ans.  17.32  miles.     How  far  off  could  it  be  seen  from  the  top  of  a 
vessel's  mast  100  feet  high  ?     Ans.  29.56  miles.     (How  far  towards 
the  light-house  could  the  surface  of  the  water  be  seen  from  the  top  of 
the  mast?     Then,  if  one's  eye  were  placed  there,  how  much  farther 
would  it  be  to  the  light-house  ?) 

12.  Why  is  it  easier  to  lift  a  stone  under  water  than  to  lift  the 
stone  in  the  air  ? 

13.  The  specific  gravity  of  quartz  (commonly  called  flint)  is  about 
2.5.     A  boy  can  lift  120  pounds  :  how  heavy  a  quartz  rock  can  he 
raise  to  the  surface  of  a  creek  ?     Ans.  200  pounds. 

14.  A  piece  of  copper  weighs  1100  grams,  and  in  water  it  weighs 
975  grams  :  find  its  specific  gravity. 

15.  A  piece  of  wood  weighs  3  ounces  ;  a  bit  of  lead  weighing  2 
ounces  in  water  will  just  keep  the  wood  totally  immersed  :  find  the 
specific  gravity  of  the  wood.     Ans.  .6. 

16.  A  water-tight  box  is  6  inches  long  and  3   inches  wide.     A 
bunch  of  keys  raises  the  water  in  it  \  inch :   what  is  the  volume  of 
the  keys  ?     If  your  hand  raises  the  water  ^  inch,  what  is  its  volume  ? 

17.  A  cylindrical  cork  floats  vertically  with  1  inch  above  the  water 
and  T3Q  of  an  inch  below :  find  the  specific  gravity. 

18.  The  specific  gravity  of  a  body  is   17 :  find  the  volume  of  89 
ounces  of  it. 

19.  A  cup  when  empty  weighs  6  ounces ;  when  full  of  water  it 
weighs  16  ounces  ;  when  full  of  coal-oil  it  weighs  14|  ounces  :  find 
the  specific  gravity  of  the  coal-oil. 

20.  A  wooden  hydrometer,  1  inch  square,  sinks  9  inches  in  water, 
but  11  inches  in  oil :  find  the  specific  gravity  of  the  oil. 

21.  A  boat  in  a  river  displaces  8000  cubic  feet  of  water  ;  on  reach- 
ing the  ocean  it  rises  so  as  to  displace  only  7800  cubic  feet:  find  the 
specific  gravity  of  sea- water  and  the  weight  of  the  boat.     Answers, 
1.026-.    250  tons. 

22.  The  specific  gravity  of  cork  is  .24 :  what  is  the  volume  and 
what  the  weight  of  a  cork  that  must  be  attached  to  a  piece  of  lead 
weighing  5  ounces  in  water,  in  order  that  both  in  the  water  may 
weigh  0  ? 

23.  A  flask  weighs  960  grains,  and  it  will  hold  2000  grains  of  water. 
Some  powdered  chalk  weighs  50  grains  in  the  air.     When  placed  in 
the  flask  and  the  flask  filled  up  with  water,  its  weight  is  2990  grains. 
Find  the  specific  gravity  of  the  chalk. 


SECTION  II.— HYDRAULICS. 

156.  Flow  of  Liquids  through  Openings. — We  have  learned 
in  Art.  96  that,  discarding  the  resistance  of  the  air,  a  body 
which  has  fallen  from  any  height  has  just  the  velocity  with 
which  a  body  would  have  to  be  sent  upward  to  reach  that 
height.  And  we  also  know  that  a  fountain,  if  the  resist- 
ance of  the  air  and  friction  did  not  hinder  it,  would  rise  to 


84 


NATURAL   PHILOSOPHY. 


the  level  of  the  water  in  the  reservoir.  It  must  be  true, 
then,  that  water  flows  out  of  an  opening  with  the  same  velocity 
that  it  would  acquire  in  falling  from  the  level  of  the  water  to 
the  opening. 

Therefore  the  formula  v  =  1/2*75"  (Art.  95)  gives  the  ve- 
locity of  discharge.  This  velocity  does  not  increase,  then, 
in  proportion  to  the  depth,  but  in  proportion  to  the  square 
root  of  the  depth.  In  order  that  the  liquid  may  flow  out 


D  C          B  A 

FIG.  71.— VELOCITY  OF  JETS. 

twice  as  fast,  the  second  opening  must  be  4  times  as  deep  as 
the  first,  and  9  times  as  deep  if  it  is  to  flow  3  times  as  fast.1 
If  an  opening  be  made  in  the  side  or  bottom  of  a 
vessel  containing  water,  the  stream  which  runs  out 
will  grow  narrower  for  a  little  way  after  it  leaves 
the  opening,  and  then  spread  out  again.  The  nar- 
rowest part  of  the  stream  is  called  the  vena  con- 
tracta  (Latin,  contracted  vein).  Its  cause  may  be 
seen  by  scattering  a  little  chalk-dust  in  the  vessel, 
which  will  be  carried  along  by  the  currents  of  water 
FIG.  72.  —  FLOW  OF  and  show  that  these  currents  rush  towards  the 

LIQUIDS     THROUGH  .  11  :«_    1*1  T  •        -rt-         wo 

AN  OPENING.  opening  from  all  directions,  as  shown  in  Fig.  72. 

And  they  keep  on  converging  a  little  way  beyond 

the  opening  and  make  the  vena  contracta  there.     On  this  account  the 

quantity  of  water  which  ought  to  be  discharged  at  a  certain  opening 

1  Before  the  invention  of  clocks,  time  was  almost  universally  meas- 
ured by  the  descent  of  water  in  a  tall  vessel  which  had  a  small  open- 
ing at  the  bottom.  This  was  called  a  clepsydra.  If  the  opening  is 


LIQUIDS.  85 


is  never  reached  in  practice,  nor  is  the  calculated  velocity  ever  quite 
reached,  on  account  of  the  friction.  The  range  of  the  spouting  liquid 
may  be  found  by  multiplying  the  velocity  of  discharge  by  the  number 
of  seconds  which  it  has  to  flow  before  striking  the  ground.  This  last 
is  the  same  as  the  time  in  which  a  body  would  fall  to  the  ground 
from  the  height  of  the  opening.  For  example,  in  Fig.  71  the  water 
flows  from  the  middle  orifice  with  a  velocity  of  9.8  feet  per  second. 
As  this  orifice  is  3  feet  from  the  ground,  the  time  of  falling  from 
there  to  the  ground  is,  by  Art.  95, 


.-.  the  range  =  9.8  feet  X  .45=  4.410  feet  (=ad  in  Fig.  71). 
The  range  from  the  opening  1  foot  above  the  middle  one  is 


2  X  4 
32.2 

For  the  one  1  foot  below  the  middle  one  we  have 


8  feet  X  A/  =  8  feet  X  -50  =  4  feet. 

\ 


11.4  feet  X  x/2X2   =  H.4  feet  X  -35  =  4  feet. 
Y'    32.2 

We  find  here  that  the  jet  which  spouts  out  half-way  up  the  column 
of  water  has  the  greatest  range  of  all,  and  the  two  spouting  out  at 
equal  distances  above  and  below  the  middle  one  have  the  same  range.1 
These  are  universal  laws,  and  can  be  rigidly  demonstrated. 

157.  Flow  through  Pipes. — A  very  short  pipe  discharges 
more  water  from  a  vessel  than  an  opening  in  the  side  of 
the  vessel  without  the  pipe,  for  the  water  tends  to  follow 
the  side  of  the  pipe,  and  the  vena  contracta  is  not  so  small. 
But  a  long  pipe  greatly  retards  the  flow.  A  long  hose-pipe 

made  just  large  enough  to  empty  the  vessel,  after  it  has  been  filled  1 
inch  deep,  in  an  hour,  it  must  be  4  inches  deep  to  run  2  hours,  9 
inches  deep  to  run  3  hours,  16  inches  deep  to  run  4  hours,  etc.  Or 
the  lowest  hour-mark  would  be  1  inch  high,  the  next  3  inches  above 
that,  the  third  5  inches  above  that,  etc.,  the  spaces  between  the  hour- 
marks  increasing  as  the  odd  numbers.  This  depends  upon  the  prin- 
ciple of  falling  bodies,  given  in  Art.  94. 

1  The  student  may  have  found  that,  if  carried  out,  the  second 
decimal  places  in  the  second  and  third  results  will  not  agree.  This  is 
because  the  decimal  places  in  the  velocity  and  time  of  fall  were  not 
carried  out  far  enough.  If  carried  out,  they  will  agree  exactly.  Will 
the  resistance  of  the  air  interfere  with  the  above  conclusions  ? 

8 


NATURAL  PHILOSOPHY. 


illustrates  this  well.     Bends  in  a  pipe  check  the  flow  very 
much,  and  a  sharp  corner  much  more  than  a  curved  bend. 

158.  Flow  of  Streams, — The  friction  of  the  sides  and  bot- 
tom retards  streams  very  much,  otherwise  all  our  streams 
would  be  raging  torrents.     Small  streams  may  fall  rapidly, 
but  the  great  rivers  of  the  world  have  a  fall  of  only  a  few 
inches  per  mile,  and  flow  from  2  to  5  miles  per  hour. 

The  Mississippi l  from  its  source  to  its  mouth  has  an  average  fall 
of  but  7  inches  to  the  mile,  and  in  the  lower  half  of  its  length  of 
about  half  of  this.  In  the  last  3000  miles  of  its  course  the  Amazon 
falls  less  than  1  inch  per  mile. 

159.  Waves.— Throw  a  pebble  into  a  still  pond  or  a  pud- 
dle of  water,  and  a  wave  is  made  which  runs  to  the  shore. 
The  most  important  fact  to  be  noticed  about  this  wave  is 
that,  while  the  wave  moves  forward,  the  particles  of  water  do 
not  move  forward,  but  each  particle  in  its  turn  simply  moves  up 
and  down.     This  can  be  seen  by  watching  a  chip  floating 
in  the  water  at  some  little  distance  from  the  edge.     The 
chip  will  rise  and  fall  with  the  water,  but  will  not  come  to 
the  shore.     If,  however,  the  chip  be  only  a  few  inches  from 
a  sloping  edge  of  the  pond,  it  will  presently  be   driven 
ashore,  for  the  water  growing  shallower  causes  some  for- 
ward motion  along  the  shore. 

It  may  not  be  easy  to  see  how  the  wave  can  move  for- 
ward while  the  water  only  moves  up  and  down.  If  you 
will  take  a  piece  of  rope  and  tie  one  end  to  a  nail,  or  let  a 

1  A  question  which  is  both  interesting  and  profitable  is  often  asked 
as  to  whether  the  Mississippi  flows  up-hill.  As  this  river  is  in  the 
northern  hemisphere  and  flows  from  north  to  south,  on  account  of 
the  bulging  out  of  the  earth  as  we  approach  the  equator  (or  its  flat- 
tening towards  and  at  the  poles),  its  mouth  is  2J  miles  farther  from 
the  centre  of  the  earth  than  its  source,  and  is  therefore  that  much 
higher  than  the  source.  But  the  mouth  of  the  river  is  on  a  much 
larger  circle  of  latitude  than  the  source,  and  must  therefore  revolve 
through  a  considerably  larger  circle  in  the  twenty-four  hours.  This 
causes  greater  centrifugal  force  at  the  mouth,  which  compensates  for 
its  greater  distance  from  the  centre  of  the  earth. 


LIQUIDS.  87 


companion  hold  it,  and,  holding  the  other  end  in  your 
hand,  give  it  a  jerk,  just  such  a  wave  as  has  been  described 
above  will  run  along  the  rope,  while  each  particle  of  the 
hemp  has  moved  only  up  and  down.  And  very  likely  you 
have  often  seen  a  wave,  caused  by  the  wind,  run  across  a 
field  of  grass  or  standing  grain,  which  you  see  must  be 
caused  in  this  way.  The  great  waves  of  the  ocean,  some- 
times thirty  feet  high,  are  caused  by  the  action  of  the  wind 
upon  the  surface  of  the  water.  Like  the  waves  in  the 
pond,  they  are,  out  at  sea,  only  upward  and  downward  mo- 
tions of  the  water ;  along  a  sloping  shore  they  get  a  for- 
ward motion,  and  become  breakers.  The  highest  part  of  a 
wave  is  called  its  crest.  The  hollow  is  the  trough.  The 
distance  from  crest  to  crest,  or  from  any  part  of  a  wave  to 
the  corresponding  part  of  the  next  one  (called  correspond- 
ing phases),  is  the  length  of  the  wave.1 

If  two  waves  were  to  meet  each  other  so  that  the  two 
crests  met,  one  would  be  piled  upon  the  other,  and  a  crest 
higher  than  either  would  be  formed.  But  if  the  crest  of 
one  meets  the  trough  of  the  other  it  will  fill  the  trough, 
and,  if  the  waves  are  of  the  same  size,  smooth  water  will  be 
the  result. 

WATEK   MACHINES. 

160.  Water- Wheels. — These  familiar  machines  are  of 
great  value.  In  all  cases  their  power  is  caused  by  water 
falling  from  a  higher  to  a  lower  level.  In  the  dam,  or  head- 
race,2 which  may  be  twenty  feet  above  the  tail-race,2  the 
water  has  potential  energy.  In  falling,  its  energy  is  actual, 
and  this  it  communicates  to  the  wheel,  and  thence  to  the 
machinery.3  Four  kinds  of  water-wheels  are  usually  de- 
scribed. 

1  It  is  important  that  what  is  said  here  about  waves  should  be 
clearly  understood,   for   they  play  an  important  part  later  in  the 
book. 

2  Find  out  what  these  are,  if  you  do  not  know. 

3  Does  the  water  ever  get  back  to  the  dam  again  ? 


88 


NATURAL   PHILOSOPHY. 


161.  The  Overshot-Wheel. — This   is  probably  the   most 
common  of  all  the  water-wheels.     As  shown  in  Fig.  73,  in 
the  circumference  of  the  wheel  are  what  are  called  buckets, 
into  which  the  water  runs  from  above  (hence  its  name), 

and  the  weight  of  the 
water  in  the  buckets 
turns  the  wheel.  Some 
of  the  objections  to  the 
overshot -wheel  are  its 
cumbersomeness,  the  loss 
of  water  from  the  buckets 
on  their  way  down,  and 
its  liability  to  freeze  up 
in  winter  in  Northern 
latitudes.  Yet  very  many 
manufacturers  still  prefer 
it  to  any  other  water- 
wheel.  Under  favorable  circumstances,  overshot-wheels 
may  utilize  75  per  cent,  of  the  potential  energy  of  the 
water. 

162.  The  Breast- Wheel. — This  wheel  is  shown  in  Fig.  74. 
It  is  sometimes  used  where  there  is  but  a  short  fall  of 


FIG.  73. — OVERSHOT-WHEEL. 


FIG.  74.— BREAST-WHEEL. 


water.  Both  the  weight  and  the  momentum  of  the  water 
aid  in  producing  the  power.  Under  the  best  circumstances, 
the  breast-wheel  utilizes  65  per  cent,  of  the  water-power. 


LIQUIDS.  89 


163.  The  Undershot-Wheel. — This  is  the  most  inefficient 
of  all  the  water-wheels,  generally  utilizing  only  about  30 
per  cent,  of  the  power.  It  is  only  adapted  to  streams 
having  a  strong  current  and  but  little  fall,  and  is  seldom 
used  at  all. 


FIG.  75.— UNDERSHOT-WHEEL.  FIG.  76.— TURBINE-WHEEL. 

164.  The  Turbine l  Water- Wheel. — This  is  a  water-wheel 
of  modern  invention,  and  was  first  used  in  France.  It  is 
an  iron  wheel  with  curved  paddles,  as  shown  in  Fig.  76. 
This  wheel  is  set  into  an  iron  case  with  its  axis  vertical.  Fig. 
77  shows  the  case  with  the  wheel  inside  but  hidden  from 
view.  The  water  passes  through  the  openings  a,  ft,  c,  etc., 
in  this  case,  and  strikes  the  paddles  of  the  wheel  within, 
thus  driving  the  wheel  around.  <  After  giving  all  its  force 
to  the  wheel,  the  water  drops  through  a  large  opening  in 
the  bottom  of  the  case  and  flows  away.  Unlike  the  first 
three  wheels,  the  turbine  revolves  horizontally,  not  verti- 
cally. 

The  encased  wheel  is  often  set  in  an  outer  iron  case,  as 
seen  in  Fig.  78.  This  is  attached  to  a  wooden  or  iron  tube 
(Fig.  79),  which  brings  the  water  from  the  head-race. 

1  Pronounced  tur'bin. 
8* 


90 


NATURAL  PHILOSOPHY. 


Turbine-wheels  are  all  comparatively  small.  They  are 
made  as  small  as  1  foot  or  less  in  diameter,  and  are  very 
seldom  more  than  6  feet  in  diameter.  The  turbine- wheels, 
being  always  entirely  under  water,  do  not  freeze  up  in 
winter,  and  they  utilize  more  of  the  power  of  the  water, 
reaching  80  or  more  per  cent,  of  it.  On  these  accounts 
many  of  them  are  now  in  use,  and  they  seem  likely  to 
supplant  almost  entirely  the  other  forms  of  water-wheels. 


FIG.  77. — TURBINE-WHEEL  IN  ITS  INNER  CASE. 


FIG.  78.— THE  OUTER  CASE. 


165.  The  Hydraulic  Ram. — This  is  a  machine  in  common 
use  for  raising  water.  The  way  in  which  it  works  may  be 
explained  by  reference  to  Fig.  80.  A  is  a  large  supply-pipe 
leading  down  from  a  spring  or  other  constant  source  of 
water.  At  C  is  a  valve  which  falls  down  of  its  own  weight 
and  leaves  an  opening  above  it.  When  the  water  begins 
to  flow  through  A,  it  escapes  at  C,  but  quickly  acquires 
velocity  enough  to  raise  the  valve  there,  and,  by  pressing  it 
against  the  top,  to  close  that  opening.  As  the  water  in  A 
is  running  with  considerable  momentum,  and  as  the  water 


LIQUIDS. 


91 


cannot  be  compressed  in  the  lower  part  of  the  pipe  (Art. 


FIG.  79.— THE  TURBINE-WHEEL  AT  WORK. 


131),  it  lifts  the  valve  B  and  rushes  up  into  the  air-chamber 
D,  compressing  the  air  into  the  upper  part  of  the  air-cham- 


92  NATURAL   PHILOSOPHY. 

ber  until  the  flow  ceases.  Then  the  valve  C  falls  again, 
and  the  same  process  is  repeated.  The  compressed  air  in 
the  air-chamber,  by  constantly  pressing  upon  the  water 
below  it,  drives  the  water  up  the  small  pipe  EF  in  a  con- 
stant stream.  This  machine  will  work  for  months  without 
any  attention,  but  the  water  gradually  absorbs  and  carries 
off  the  air  in  the  air-chamber,  so  that  occasionally  a  new 


FIG.  80.— THE  HYDRAULIC  HAM. 

supply  must  be  admitted.  The  pipe  A  need  have  only 
a  few  feet  of  fall,  and  water  may  HI  this  way  be  raised 
through  EF  to  a  considerable  height.  The  repeated  shock 
and  noise  caused  by  the  lifting  of  C  has  been  thought  to 
resemble  the  butting  of  a  ram,  hence  the  curious  name  of 
this  machine. 

166.  Barker's  Mill.— This  scientific  toy  is  shown  in  Fig. 
81,  It  consists  of  an  upright  tube,  c,  near  the  bottom  of 
which  are  two  smaller  tubes  extending  out  on  opposite 
sides  of  the  upright  tube ;  near  the  ends  of  these,  but  on 
opposite  sides,  are  two  small  openings.  The  pressure  from 
the  column  of  water  in  c  is  relieved  at  the  openings,  but  it 
presses  against  the  sides  of  the  tubes  opposite  the  openings, 


LIQUIDS.  93 


and  hence  moves  the  machine  around  in  that  direction,  or 
opposite  to  the  direction  in  which  the  water  spouts. 

The  joints  of  a  cane  fishing-pole  will  furnish  excellent  material,  in 
the  hands  of  an  ingenious  boy,  to  make  a  Barker's  Mill. 


FIG.  81. — BARKER'S  MILL 

Exercises. — 1.  Verify  the  velocities  of  the  different  jets  in  Tig.  71. 

2.  Find  the  velocity  of  a  jet  of  water  through  an  opening  10  feet 
below  the  surface  ;  20  feet  below. 

3.  Find  the  range  in  each  case  in  the  preceding  problem,  if  the 
surface  of  the  water  in  the  vessel  be  30  feet  from  the  ground. 

4.  Making  no  allowance  for  the  vena  contracta,  how  much  water 
would  be  discharged  through  the  lowest  opening  in  Fig.  71  in  1  min- 
ute if  the  opening  is  1  inch  square  and  the  surface  of  the  water  be 
kept  at  the  same 'height? 

Solution.—    17.9  feet  =  214.8  inches,  velocity  per  second. 
214.8  X  60  =  12, 888  inches,  velocity  per  minute. 
As  the  jet  flows  12,888  inches  per  minute,  a  column  of  water  1  inch 
square  and  12,888  inches  long  flows  out  in  1  minute,  that  is,  12,888 
cubic  inches.     As  there  are  231  cubic  inches  in  a  gallon, 
12,888  -5-  231  =  55$ \  gallons. 

5.  The  area  of  the  vena  contracta  is  usually  about  |  of  the  orifice  : 
supposing  this  to  be  the  true  cross-section  of  the  stream,  what  would 
be  the  flow  per  minute  in  Exercise  4  ?     Ans.  34f  £  gallons. 

6.  If  in  Exercise  2  each  opening  is  a  circle  1  inch  in  diameter, 
how  many  gallons  will  flow  out  of  each  in  1  minute,  no  allowance 
being  made  for  the  vena  contracta  ? 

7.  What  would  be  the  discharge  in  Exercise  6  if  the  vena  contracta 
be  allowed  for  as  being  f  of  the  area  of  the  orifice  ? 

8.  Why  is  a  stream  swifter  in  the  middle  than  near  the  banks  ? 

9.  Why  does  the  water  of  a  stream  flow  so  much  faster  during  a 
flood  than  usual  ? 


94  NATURAL   PHILOSOPHY. 


10.  What  would  be  the  effect  if  the  water  were  allowed  to  fall 
upon  an  overshot- wheel  directly  over  the  axis  ? 

11.  Which  side  of  the  point  mentioned  in  Exercise  10  had  the  water 
better  be  allowed  to  fall  upon  ? 

12.  Why  would  it  not  do  for  the  small  pipe  to  open  into  the  top  of 
the  air-chamber  of  the  hydraulic  ram  ? 


GASES.  95 


CHAPTEE    IV. 
GASES. 

167.  Definition  and  Properties. — As  we  have  before  learned 
(Art.  26),  gas  is  that  form  of  matter  in  which  the  molecules 
have  a  repellent  action  upon  one  another.     A  gas  will  ex- 
pand indefinitely  if  it  has  room  to  do  it  in.     A  thimbleful 
of  air,  if  put  into  an  absolutely  empty  room,  would  fill  the 
whole  room.     The  force  with  which  a  gas  tries  to  expand 
is  its  tension. 

All  liquids,  and  even  some  solids,  are  constantly,  though 
perhaps  slowly,  changing  to  gas,  which  disappears  by 
spreading  itself  through  the  air.  This  is  called  evaporation, 
and  the  gases  into  which  the  solids  or  liquids  turn  are 
called  their  vapors.  By  the  application  of  heat  almost 
every  solid  has  been  liquefied  and  then  changed  to  vapor 
or  gas.  On  the  other  hand,  all  the  gases  have  by  cold  and 
pressure  been  changed  into  liquids  or  solids. 

Until  1877,  air  and  several  other  of  our  most  common  gases  resisted 
all  efforts  to  change  their  gaseous  form ;  but  in  that  year  two  European 
scientists,  by  means  of  great  cold  and  enormous  pressure,  liquefied  or 
solidified  all  of  these  gases  which  were  formerly  called  permanent. 

168.  Compressibility  of  Gases. — We   found  that  liquids 
were  almost  absolutely  incompressible.     Gases,  on  the  con- 
trary, are  easily  compressed. 

Experiment  33. — Press  a  tumbler,  top  down,  into  a  basin  of  water. 
As  it  is  pushed  deeper,  the  water  can  be  seen  to  rise  somewhat  in  the 
mouth  of  the  tumbler.  The  pressure  of  the  water  is  compressing  the 
air.  The  resistance  you  feel  is  the  tension  of  the  compressed  air. 

169.  Mariotte's '  Law. — Fig.  82  shows  a  piece  of  appa- 

1  Ma-re-ot'  (1620-1684),  a  French  scientist. 

This  law  was  first  discovered  by  an  Irish  scientist,  Kobert  Boyle 


96  NATURAL   PHILOSOPHY. 

ratus  used  for  making  more  careful  experiments  in  com- 
pressing air.  A  little  mercury  is  poured  into  the  open  end 
of  the  glass  tube,  and  the  air  from  the  short  end  of  the 
tube  is  allowed  to  escape  by  tilting  the  tube 
until  the  mercury  stands  on  a  level  in  both 
arms  at  a.  The  air  in  the  short  arm  is  now 
at  its  natural  density,  and  is  pressed  upon 
only  by  the  weight  of  the  atmosphere  itself. 
This  weight  is  equal  to  about  30  inches  of 
mercury,  as  we  shall  see  in  the  next  article. 
More  mercury  is  now  poured  into  the  long 
arm,  until  it  is  about  30  inches  higher  there 
than  in  the  short  arm,  when  the  air  in  the 
short  arm  (ab~)  will  be  found  to  be  compressed 
into  one-half  its  former  bulk  (mb).  There  is 
double  the  pressure  upon  it  (one  atmosphere 
of  air  and  one  of  mercury),  which  has  com- 
pressed it  one-half.  If  one  column  be  made 
60  inches  higher  than  the  other,  the  air  in  the 
short  arm  will  be  compressed  into  the  upper 
third  of  ab  ;  it  is  pressed  down  by  three  atmos- 
pheres.  90  inches  of  mercury  (making  with 


FIG.  82.—  APPARA-  ^ne  air  four  atmospheres)  will  compress  the 

TU8     ILLUSTRAT-  r  . 

ING  MARIOTTE'S  a|r  in   the  short  arm  into  one-fourth  of  its 

LAW. 

original  bulk.  Hence  we  see  that  the  bulk  of 
a  quantity  of  air  is  decreased  just  as  the  pressure  upon  it  is 
increased.  This  law  is  substantially  true  of  all  the  gases. 

Questions.—  When  the  mercury  is  30  inches  higher  than  c,  is  it  30 
inches  higher  than  in  the  short  arm  ? 

If  ab  is  6  inches,  how  much  above  c  will  the  long  column  reach 
when  30  inches  higher  than  the  short  one?  Ans.  33  inches. 

How  many  inches  of  mercury  must  be  poured  in  to  raise  it  as 
above?  Ans.  36  inches. 

What  will  be  the  answers  of  the  last  two  questions  if  the  mercury 
in  one  tube  is  60  inches  higher  than  in  the  other  ? 

(1626-1691),  but  was  afterwards  independently  discovered  by  Mariotte, 
and  hence  usually  goes  under  his  name. 


GASES. 


97 


170.  Column  of  Mercury  supported  by  the  Air.— Experi- 
ment 34.— Take  a  glass  tube,  1  yard  long,  |  or 

£  of  an  inch  in  diameter,  one  end  of  which  is 
closed,  fill  it  with  mercury,  place  the  finger  over 
the  open  end,  and  invert  it,  as  shown  in  Fig.  83. 
Lower  the  tube  until  the  open  end  is  covered 
by  the  mercury  in  the  pan  below,  then  remove 
the  finger.  The  mercury  in  the  tube  will  sink 
until  it  is  about  30  inches  high,  then  it  will 
stand  there,  being  just  balanced  by  the  pressure 
of  the  air  upon  the  surface  of  the  mercury  in 
the  basin.  We  have  found  that  a  column  of  mer- 
cury 30  inches  high  weighs  the  same  as  a  column 
of  air  of  the  same  thickness,  extending  from  the 
surface  of  the  earth  to  the  top  of  the  atmos- 
phere.1 

When  proper  precautions  have  been  taken  to 
have  the  mercury  pure  and  to  remove  all  bub- 
bles of  air  from  the  tube,  the  space  above  the 
mercury  is  almost  a  perfect  vacuum.  But  yet 
there  is  a  little  vapor  of  mercury  there.  An 
absolute  vacuum  has  never  been  made. 

Why  does  the  experiment  not  show  that  the 
column  of  mercury  balances  (and  therefore 
weighs  as  much  as)  a  column  of  air  as  large 
around  as  the  basin  ?  (See  Art.  134.) 

171.  The  Barometer. — If  the  glass  tube 
and  the  basin  of  mercury  just  described 
be  enclosed  in  a  suitable  case,  and  a  scale 
of  inches  and  fractions  be  made  on  a 
part  of  the  upper  end  of  the  tube,  we 
have  a  barometer,  an  instrument  which 
will  indicate  the  changes  in  the  pressure 
(i.e.,  the  weight)  of  the  air  at  that  place, 
which  makes  it  a  very  important  instru- 
ment. 

172.  Height  of  Mountains   measured 

TTT1          -r,  i  ,  i      FIG.  83. — BAROMETER  IN 

with  the  Barometer. — When  Pascal  heard        ITS  SIMPLEST  FORM. 


1  The  height  of  the  column  of  mercury  may  vary  a  little  from  30 
inches,  showing  that  the  weight  of  a  column  of  the  atmosphere 


varies. 
E 


9 


9 


98 


NATURAL   PHILOSOPHY. 


of  the  experiment  described  in  Art.  170,  he 
said  that  if  it  was  the  weight  of  the  air  that 
held  the  mercury  30  inches  high  in  the  tube, 
were  he  to  carry  the  basin  and  tube  to  the 
top  of  a  mountain  the  mercury  would  fall 
below  30  inches,  for  there  would  not  be  so 
much  air  above  it  there.  It  was  tried,  and, 
as  Pascal  expected,  as  the  tube  was  taken  up 
the  mountain  the  top  of  the  column  of  mer- 
cury slowly  went  down,  a  convincing  proof 
that  it  was  the  weight  of  the  atmosphere 
which  was  supporting  the  mercury.  Bar- 
ometers are  now  very  commonly  used  to 
measure  the  heights  of  mountains.  For  low 
mountains  the  mercury  falls  1  inch  for  about 
every  900  feet  of  height.  At  a  height  of  3^ 
miles  the  mercury  is  15  inches  high.1  Half 
of  the  atmosphere  is  therefore  within  3£ 
miles  of  the  surface  of  the  earth. 

173.  The  Barometer  and  the  Weather. — 
The  most  common  and  valuable  use  of  the 
barometer  is  to  enable  us  to  foretell  the 
weather :  hence  it  is  often  called  a  weather- 
glass. Any  sudden  change  in  the  height  of 
the  mercury  is  almost  always  followed  by  a 
storm,  and  usually  it  falls  rapidly  before  a 


FIG.  84. — THE  MER- 
CURIAL BAROMETER. 


1  The  following  table   shows   the   height  of  the 
mercury  at  different  distances  above  the  earth  : 

HEIGHT  ABOVE  HEIGHT  OF 

THE  EARTH.  MERCURY. 

1  mile 24.7  inches. 


2  miles 20.3 


4 

5 

10 
15 
20 


.16.7  " 
13.7  " 
.11.3  " 
.  4.2  " 
.  1.6  " 
,  1  inch  (or  less). 


GASES. 


99 


storm.     This  will  be  explained  and  more  fully  discussed  in 
the  chapter  on  Meteorology. 

174.  The  Aneroid  Barometer. — Fig.  85  shows  the  aneroid 
barometer,  very  different  from  the  mercurial  barometer, 
and  much  used  now.  It  is  a  thin  metal  box,  from  which 
the  air  is  partly  exhausted  and  it  is  then  made  air-tight. 
The  top  of  the  box  is  pressed  down  more  or  less,  accord- 


Fia.  85. — THE  ANEROID  BAROMETER. 

ing  as  the  pressure  of  the  atmosphere  varies ;  this,  by 
means  of  levers,  causes  a  hand  to  move  back  or  forth, 
which  indicates  the  pressure.  In  the  figure  the  metal  box 
is  seen  within  the  outside  case  and  behind  the  levers.  It 
is  graduated  by  comparing  it  with  a  mercurial  barometer. 
The  aneroid  barometer  is  very  convenient  to  carry  and  use, 
for  it  is  sometimes  made  no  larger  than  a  watch.  It  is  also 


»- 

DEPARTMENT  OF  PHYS 

100  NATURAL   PHILOSOPHY. 


very  delicate,  but  is  liable  to  get  out  of  order,  and  should 
frequently  be  compared  with  a  mercurial  barometer. 

THE   ATMOSPHERE. 

175.  Composition  of  the  Atmosphere. — The  atmosphere 
is  composed  mainly  of  two  gases, — oxygen  and  nitrogen. 
These  gases  are  not  chemically  united  in  the  atmosphere, 
as  oxygen  and  hydrogen  are  in  water,  but  are  simply  mixed 
together  in  the  proportion  of  four  parts  of  nitrogen  to  one 
of  oxygen.     There  is  always  vapor  of  water  also  in  the 
atmosphere,  as  well  as  small  quantities  of  other  gases. 

176.  Height  of  the  Atmosphere.— The  height  of  the  atmos- 
phere is  unknown.     From  calculations  depending  upon  the 
duration  of  the  twilight  it  was  formerly  supposed  that  the 
atmosphere  was  about  45  miles  high.     But  this  only  proved 
that  if  there  were  air  above  that,  it  was  not  dense  enough 
to  cause l  twilight.     And  recent  observations  of  meteors 2 
(shooting-stars)  show  that  the  atmosphere  is  at  least  100 
miles  high.     One-half  of  the  whole,  however,  is  within  the 
first  3J  miles,  and  the  upper  part  must  be  excessively  rare. 

177.  Weight  of  the  Atmosphere.— The  atmosphere  must 
weigh  as  much  as  an  ocean  of  mercury  covering  the  whole 
earth  to  a  depth  of  2£  feet.     This  is  almost  six  quadrillion 
tons.8     The  air  in  a  room  25  feet  long,  20  feet  wide,  and  10 
feet  high  weighs  nearly  400  pounds. 

178.  Pressure  of  the  Air. — A  column  of  mercury  1  inch 

1  Twilight  is  the  reflection  of  the  sun's  light  from  the  upper  part 
of  the  atmosphere.   (Sharpless  and  Philips's  Astronomy,  p.  116.) 

2  Meteors,  or  shooting-stars,  are  small  solid  particles  of  matter 
moving  in  orbits  around  the  sun.    When  these  strike  our  atmosphere 
their  velocity  is  so  great  that  the  heat  produced  by  the  blow  burns 
them  up,  and  it  is  the  flash  of  this  burning  that  we  see.     The  obser- 
vations referred  to  above  show  that  some  of  them  begin  to  burn  100 
miles  or  more  high  :  hence  the  atmosphere  must  extend  to  that  height. 
(See  Astronomy,  chapter  viii.) 

8  Verify  this,  taking  13.6  to  be  the  specific  gravity  of  mercury. 


GASES. 


101 


square  and  2£  feet  high  weighs  about  15  (14.7)  pounds. 
Therefore  the  atmosphere  everywhere  presses  down  with 
a  force  of  15  pounds  to  the  square  inch.  And,  as  is  the  case 
with  water,  this  pressure  is  the  same  in  all  directions. 

Everything  about  us  is  subjected  to  this  enormous  pressure.  The 
average  human  body  has  a  surface  of  about  gOOO  square  inches,  and 
therefore  sustains  a  pressure  of  15  tons.  We!  fejfe  io=sis^ious  ct  n6 
downward  pressure,  because  the  air  beneath*  presses3  us"  up  just  the 
same.  And  the  human  body,  largely  filled*  \utth;  liquids  =ai<}  air,  }s; 
firm  enough  to  resist  the  crushing  pressur5J6f>'r5*p0aBcis  to  tho  square 
inch  when  distributed  all  over  it. 

179.  Experiments  with  the  Pressure  of  the  Air.— Experi- 
ment 35. — Dip  a  tumbler  under  water  in  such  a  way  that  all  the  air 
may  escape  and  it  shall  be  full  of  water.  Kaise  the  tumbler  partly 
out  of  the  water,  bottom  upward,  keeping  the  edge  under  water.  Is 
the  part  of  the  tumbler  above  the  water  empty  ?  Explain. 

Experiment  36. — Fill  a  tumbler  full  of  water.  Cover  the  top  with 
a  card  or  piece  of  heavy  paper,  and,  pressing  this  tightly  against  the 
top,  invert  the  tumbler.  Remove  the  hand  from  the  card,  and  the 
upward  pressure  of  the  air  will  hold  the  card 
against  the  inverted  tumbler  and  keep  the  water 
in  it. 

Experiment  37. — Make  a  "sucker"  by  taking 
a  round  piece  of  thick  leather,  fasten  a  string  to 
the  middle  of  it,  wet  it,  and  press  it  tightly 
against  a  brick  or  flat  stone.  As  the  air  cannot 
get  under  the  sucker,  the  downward  pressure 
holds  it  to  the  brick,  so  that  both  may  be  lifted  up 
by  the  string.  Suppose  the  sucker  stuck  perfectly 
air-tight  and  had  a  surface  of  4  square  inches, 
how  heavy  a  stone  could  be  picked  up  with  it  ? 

Experiment  38. — Fig.  86  shows  a  pipette  ;  the 
opening  at  the  bottom  is  very  small.  Fill  it  with 
water  and  cover  the  upper  opening  with  the  fin- 
ger, the  water  will  not  run  out ;  remove  the  fin- 
ger, the  water  will  run  or  drop  out.  "Why  ? 
This  is  much  used  for  dropping  small  quantities 
of  liquids. 

Cupping. — Physicians,  in  treating  certain  dis- 
eases, sometimes  press  a  cup  to  some  part  of  the 
body  and  exhaust  part  of  the  air  from  it,  either  by 
sucking  it  out  through  a  tube  in  the  bottom  of 
the  cup,  or  by  the  burning  of  a  bunch  of  paper 
which  has  been  put  into  the  bottom  of  the  cup 
and  set  on  fire  before  it  was  applied  to  the  body.  The  skin  and  flesh 
are  sucked  up  into  the  tumbler.  This  shows  what  an  outward  press- 

9* 


FIG.  86.— PIPETTE. 


J02  NATURAL   PHILOSOPHY. 

ure  the  body  has,  in  order  to  withstand  the  enormous  pressure  of  the 
air.  (Ask  your  family  physician  to  tell  you  all  about  cupping,  so  that 
you  can  answer  your  teacher's  questions  about  it.) 

180.  Stream  of  Air  meeting  a  Surface. — When  a  current 
of  air  strikes  a  surface,  it  does  not  bound  off.  according  to 
the  law  of  incidence  and  reflection,  but  follows  along  the 
surface.    'This  is'dae  to  the  adhesion  of  the  air  to  the 
surface,  arrd  to  ~the  resistance  of  the  surrounding  air. 

.  Experiment  3§.J-iBldw'  obliquely  against  a  wall,  and  while  doing 
so  hold  a  lighted  candle  so  that  the  current  would  strike  it  were  the 
angle  of  reflection  equal  to  the  angle  of  incidence.  The  flame  will 
not  be  disturbed.  Then  hold  the  candle  close  to  the  wall  beyond  the 
place  where  the  current  strikes.  The  flame  will  be  much  disturbed, 
and  may  be  blown  out. 

Experiment  40. — Bend  a  quarter  of  an  inch  of  each  end  of  a  card 
at  right  angles  to  the  card.  Set  the  card  up  on  these  ends,  as  legs, 
upon  a  table,  and  try  to  blow  the  card  over  by  blowing  against  the 
table  under  the  card,  with  the  intention  of  making  the  air  rebound 
against  the  under  side  of  the  card.  The  air  will  not  follow  the  angle 
of  reflection,  but  along  the  table. 

Experiment  41. — Take  a  small  bent  tube  of  glass,  push  one  end 
just  through  a  wide  cork,  or  a  piece  of  wood,  so  that  the  cork  forms 
a  little  platform  about  the  end  of  the  tube.  Put  a  pin  through  a 
card,  and  lay  the  card  upon  the  cork,  letting  the  pin  run  into  the 
tube.  Now  blow  into  the  other  end  of  the  tube.  The  card  will  not 
be  blown  off,  but  will  stick  tight  to  the  cork,  and,  if  turned  upside 
down,  will  stay  there  as  long  as  the  blowing  lasts  ;  when  that  stops 
it  will  fall  off.  The  air  flowing  out  in  all  directions  between  the  cork 
and  the  card  produces  a  partial  vacuum  there,  and  the  pressure  of 
the  air  on  the  other  side  of  the  card  causes  it  to  stick  closer. 

181.  Buoyancy  of  the  Air.— All   bodies  in  the   air   are 
buoyed  up  by  it,  just  as  they  are  when  in  water,  and  are 
of  course  lightened  by  the  weight  of  the  air  displaced. 
This  is  about  1  ounce  for  each  cubic  foot  of  the  body's 
bulk,  and  is  not  therefore  noticed  except  with  very  light 
substances,  such  as  feathers  and  the  like. 

182.  Balloons. — These  are  huge  bags  of  silk,  made  air- 
tight by  varnish,  and  filled  with  hydrogen  or,  more  com- 
monly, with  common  illuminating  gas.    As  either  of  these 
is  much  lighter  than  air,  the  balloon  will  ascend  and  carry 
considerable  weight  with  it.     In  1862,  Mr.  Glaisher  (gla'- 


GASES. 


103 


sber),  of  England,  ascended  in  a  balloon  to  the  enormous 
height  of  35,000  feet,  or  nearly  seven  miles. 


FIG.  87.— BALLOON. 


PNEUMATIC   MACHINES. 

183.  The  Bellows. — The  common  hand-bellows  is  made 
of  two  tapering  boards,  joined  together  around  the  edges 
by  flexible  leather,  and  having  a  nozzle  at  one  end.  An 
opening  in  one  of  the  boards  is  covered  on  the  inside  with 
a  flap  of  leather  fastened  only  at  one  end.  This  is  a  valve ; 
it  opens  freely  inward.  When  the  sides  of  the  bellows  are 
pushed  apart,  the  air  pushes  the  valve  inward  and  rushes 
in.  But  when  the  sides  are  brought  together,  the  air 
pushes  the  valve  tight  against  the  side,  and,  thus  closing 
that  opening,  must  escape  through  the  nozzle.  The  stream 
of  air  is  not  continuous. 


104  NATURAL   PHILOSOPHY. 

Blacksmiths  use  an  improved  bellows,  which  gives  a  con- 
tinuous stream  of  air.  When  one  lets  go  of  a,  the  lower 
board  falls  and  the  air  pushes  the  valve  v  up  and  rushes  in. 

When  a  is  pushed 
down  and  be  raised,  v 
closes  and  the  air  is 
forced  through  v'  into 
an  upper  chamber. 
Upon  this  there  are 
weights  which  con- 
stantly force  the  air 

FIG.  88.— BLACKSMITHS'  BELLOWS.  OUt  of  the  nozzle. 

184.  The  Air-Pump. 

—This  very  useful  machine  was  invented  by  Otto  Guericke1 
about  1650.  Pig.  89  gives  a  complete  view  of  one  of  the 
simpler  forms  of  the  machine,  and  Fig.  90  shows  the  inside 
of  one.  In  the  common  ones  the  rod  running  up  from  S'  is 
wanting,  db  is  a  brass  cylinder,  called  the  barrel,  in  which 
an  air-tight  piston,  p,  moves  up  and  down.  When  p  is  raised 
from  the  bottom  of  the  cylinder,  a  vacuum  is  formed  below 
it,  and  the  tension  of  the  air  in  the  receiver  E  causes  it  to 
rush  along  the  tube  below,  to  push  up  the  valve  S',  and  to  fill 
the  cylinder  with  rarefied  air.  When  the  piston  is  pushed 
down,  S'  falls,  and  the  air  pushes  S  up  in  order  to  escape. 
One  barrelful  has  been  pumped  out  of  the  receiver.  The 
next  time  a  barrelful  of  rarer  air  is  taken  out,  and  that 
left  inEis  rarer.  This  can  be  kept  up  until  the  air  in  E  is 
very  rare,  until  it  is  so  rare  that  its  tension  is  too  feeble  to 
lift  the  valve  S',  but  it  is  evident  that  it  can  never  be  en- 
tirely exhausted. 

Some  of  the  more  expensive  air-pumps  have  the  rod  shown  in  Fig. 
90,  by  means  of  which  the  piston  opens  and  closes  the  valve  S'.  As 
seen  in  the  figure,  the  rod  passes  through  the  piston,  fitting  in  it 
rather  tightly.  When  the  piston  is  pushed  down,  the  rod  sticks  fast 

1  Otto  von  Guericke  (fon  ga'rik-eh),  a  German  natural  philoso- 
pher, 1602-1686. 


GASES. 


105 


in  the  piston  until  S'  is  pushed  down,  then  the  piston  slips  down 


FIG.  89.— THE  AIR-PUMP. 


around  it.     When  the  piston  is  raised,  it  lifts  the  rod  high  enough  to 
open  S',  but  cannot  lift  it  farther,  because  of  the  button  at  the  top  of 


FIG.  90.— THE  INSIDE  OF  AN  AIR-PUMP. 
the  rod.     Since  the  action  of  the  valve  S'  does  not  depend  upon  the 


106  NATURAL   PHILOSOPHY. 


tension  of  the  air  in  the  receiver,  this  pump  will  produce  a  more 
nearly  perfect  vacuum  ;  but  it  is  evident  that  this  could  not  produce 
an  absolute  vacuum,  and  the  impossibility  of  making  perfect  ma- 
chinery renders  the  vacuum  appreciably  less  perfect  than  in  theory  it 
ought  to  be. 

Air-pumps  are  often  made  with  two  barrels,  in  order  to  exhaust  the 
air  more  rapidly ;  and  many  different  forms  of  the  machine  have 
been  devised  for  the  same  purpose. 

185.  The  Air-Pump  Gauge. — In  Fig.  90,  F  is  a  gauge  to 
show  how  much  of  the  air  is  exhausted.  It  is  a  U-shaped 
tube,  closed  at  one  end,  containing  mercury,  and  enclosed 
in  an  air-tight  glass  case,  into  which  there  is  an  opening  from 
the  receiver.  Before  the  pump  begins  to  work,  the  mer- 
cury is  all  standing  in  the  closed  end  of  the  tube,  which  it 
fills  to  the  top,  and  is  kept  there,  of  course,  by  the  pressure 
of  air  down  the  open  end,  which  is  the  same  then  as  the 
pressure  of  the  air  outside.  When  part  of  the  air  has 


FIG.  91.— HAND-GLASS.  FIG.  92.— THE  BURST  FIG.  93.— MAGDEBURG 

BLADDER.  HEMISPHERES. 

been  exhausted,  the  tension  of  the  air  in  the  pump  is  not 
great  enough  to  hold  up  the  mercury  in  the  closed  tube, 
and  it  gradually  falls.  If  a  perfect  vacuum  were  made,  the 
mercury  would,  of  course,  stand  at  the  same  height  in  both 
tubes.  The  branches  of  the  tube  are  usually  only  a  few 
inches  long,  as  the  gauge  is  not  needed  until  most  of  the 
air  is  exhausted. 

Another  form  of  gauge  is  sometimes  made  by  attaching 


GASES. 


107 


a  long  glass  tube  to  the  air-pump  by  a  rubber  tube,  and 
then  putting  the  lower  end  of  the  glass  tube  in  a  vessel  of 
mercury.     As  the  air  is  exhausted,  the  mercury  will  rise 
in  the  tube. 
How  high  would  it  rise  if  the  pump  could  produce  a  perfect  vacuum  ? 

186.  Experiments  with  the  Air-Pump, — Experiment  42.— 

Take  a  hand-glass  (Fig.  91),  and  set  it  upon  the  brass  plate  of  the  air- 
pump,  in  the  place  of  the  receiver.1  Cover  the  top  of  the  glass  closely 
with  one  hand,  and  work  the  pump.  As  the  air  below  is  exhausted, 
the  pressure  of  the  air  above  is  felt,  and  presently  it  becomes  difficult 
to  remove  the  hand  from  the  top  of  the  hand-glass. 

Experiment  43. — Tie  a  piece  of  wet  bladder  tightly  around  the  top 


FIG.  94.— THE  WEIGHT-LIFTER. 


FIG.  95. — WEIGHT  IN  A  VACUUM. 


of  the  hand-glass,  or  around  the  top  of  a  bladder-glass  ;  after  drying 
it  thoroughly,  put  it  upon  the  air-pump,  and  exhaust  the  air,  the 
bladder  will  burst  with  a  loud  report :  which  way,  inward  or  outward  ? 
Experiment  44. — The  Magdeburg  hemispheres  are  two  hollow 
brass  hemispheres,  which  will  fit  very  closely  together.  After  clean- 
ing and  greasing  the  edges,  put  the  hemispheres  together,  and  screw 
fast  to  the  air-pump.  After  exhausting  the  air,  turn  the  stop-cock, 

1  Here,  as  in  all  experiments  with  the  air-pump,  unless  the  lower 
edge  of  the  glass  vessel  is  carefully  ground,  it  must  be  coated  with 
tallow,  to  keep  air  from  passing  between  it  and  the  brass  plate.  The 
edge  of  the  glass  and  the  brass  plate  should  be  cleaned  beforehand. 


108 


NATURAL   PHILOSOPHY. 


remove  from  the  air-pump,  and  screw  on  the  second  handle.  Two 
students  will  find  that  they  may  pull  hard,  yet  not  pull  the  two 
hemispheres  apart.  Turn  the  stop-cock,  and  they  fall  apart : l  why? 
Experiment  45. — Put  a  foot-ball  partly  filled  with  air,  or  a  partly- 
blown  bladder,  under  the  receiver  of  an  air-pump.  Exhaust  the  air, 
and  the  foot-ball  or  bladder  will  swell  out :  why  ?  Try  the  experi- 
ment with  raisins  or  a  shrivelled  apple  under  the  receiver. 


FIG.  96. — FOUNTAIN  IN  A  VACUUM. 


FIG.  97.— FEATHER  AND  COIN. 


Experiment  46. — "  Bursting  bombs,"  air-tight  cubes,  or  flasks  of 
thin  glass  may  be  bought  from  any  dealer  in  philosophical  apparatus. 
Put  one  under  the  receiver,  and  exhaust  the  air.  It  will  burst  with 
considerable  force.  Explain. 

Experiment  47. — Attach  the  top  of  the  weight-lifter  (Fig.  94)  to 
the  air-pump  by  a  rubber  tube.  Exhaust  the  air,  and  the  weight 
will  be  drawn  up  :  why  ? 

Experiment  48. — Carefully  balance  a  good-sized  light  metal  ball, 
then  put  it  under  the  receiver,  and  exhaust  the  air.  The  ball  will  now 
be  found  to  be  heavier  than  the  weight :  why  ?  (See  Art.  181.)  For 
this  experiment  a  hollow  metal  ball  is  commonly  used.  Should  there 
be  an  opening  into  the  ball  ?  Any  light  solid  or  liquid,  such  as  a  glass 

1  The  Magdeburg  hemispheres  were  invented  by  Otto  von  Guericke, 
the  inventor  of  the  air-pump.  The  hemispheres  get  their  name  from 
the  city  in  Germany  where  the  inventor  lived.  He  made  a  very  large 
pair,  and  in  an  exhibition  before  the  Emperor  of  Germany  it  is  said 
that  several  horses  were  unable  to  pull  them  apart. 


GASES. 


109 


bottle  (should  it  be  stoppered  ?),  may  be  thus  weighed  outside  and  then 
inside  the  vacuum.  Why  ought  the  body  weighed  to  be  lighter  (less 
specific  gravity)  than 
the  weights  used?  Sup- 
pose it  were  the  same 
as  the  weights  ?  Sup- 
pose it  were  heavier  ? 

Experiment  49. — 
Unscrew  the  top  of  the 
vacuum  fountain  ap- 
paratus (Fig.  96),  screw 
it  to  the  air-pump,  and 
exhaust  the  air.  Turn 
the  stop-cock  crosswise, 
and  screw  it  into  its 
base  again.  The  pan 
at  the  bottom  is  filled 
with  water,  into  which 
a  tube,  running  up  the 
stem,  opens.  If  the  stop- 
cock be  turned,  the 
water  will  rush  up  into 
the  glass  vessel  in  a 
fountain:  why? 

Experiment  50. — • 
Fig.  97  shows  a  long, 
air-tight  glass  tube  con- 
taining a  feather  and  a 
small  coin.  Turn  the 
tube  upside  down,  and 
the  coin  will  fall  quickly 
to  the  other  end,  but 
the  feather  will  lag 
slowly  behind.  Ex- 
haust the  air  from  the 
tube,  and  try  the  same 
thing.  They  will  fall 
together  :  why  ?  (Art. 
181.) 

187.    S  p  r  e  n  g  e  1'S  FIG.  VS.— SPRENGEL'S  AIR-PDMP. 

Air-Pump, — The  im- 
perfections of  the  common  air-pump  have  already  been 
mentioned.  A  very  good  one  will  leave  y^Vir  °f  tne  a*r  *n 
the  receiver.  But  Fig.  98  represents  a  much  more  perfect 
kind  of  air-pump.  The  funnel  A  contains  mercury.  The 
long,  narrow  glass  tube  cd  opens  into  the  funnel  and  dips 
at  the  lower  end  into  the  mercury  in  the  bottle  B.  The 
receiver  E,  from  which  the  air  is  to  be  exhausted,  has  air- 

10 


110 


NATURAL   PHILOSOPHY. 


tight  connections  with  the  tube.  The  mercury  running 
down  the  tube  from  the  funnel  separates  into  drops,  because 
its  velocity  increases  as  it  falls.  Each  drop  is  an  air-tight 
piston,  and  between  the  drops  are  nearly  perfect  vacuums. 
As  one  of  these  vacuums  comes  to  x,  part  of  the  air  in  R 
rushes  out  to  fill  it,  and  that  air  is  carried  down  into  the 
bottle  B,  where  it  comes  to  the  surface  as  a  bubble  and 
disappears.  In  this  way  the  air  is  drawn  from  B  until 
almost  a  perfect  vacuum  is  formed  there.  Under  favorable 
circumstances,  this  pump  leaves  only  T>T(rJiinnr  °^  tne  a^r 
in  the  receiver. 

As  the  exhaustion  goes  on,  the  mercury  stands  higher 
and  higher  in  the  tube,  and  finally  is  about  30  inches 
above  the  spout  B.  (Why?)  With  no  intervening  air- 
spaces, the  opening  x  must  therefore  be  more  than  30  inches 
above  the  spout  B.  The  whole  apparatus  is  commonly 
about  6  feet  high,  and  the  upright  tube  is  about  T^  of 
an  inch  in  diameter.  The  process  is  slow,  especially  if 
the  receiver  be  large.  It  is  only 
by  this  pump  that  the  necessary 
vacuum  can  be  produced  in  the 
electric  lamp  of  the  present  day. 

188.  Air-Condenser, — If  the  two 
valves  in  the  barrel  of  the  air- 
pump  (Fig.  99)  were  turned  the 
other  way, — that  is,  if  both  opened 
downward  instead  of  upward, — it 
is  clear  that  every  stroke  of  the 
piston  would  drive  air  into  the 
receiver.  Such  a  piece  of  ap- 
IJj  paratus  is  called  a  condenser. 

Draw  a  section  of  a  condenser  show- 
ing the  position  of  the  two  valves  while 

FIG.  99.— THE  CONDENSER.        the  piston  is  being  raised.      Draw  an- 
other showing   them  while  it  is  being 

pushed  down.  Can  you  think  of  any  way  in  which  a  condenser  could 
be  made  with  its  piston  solid,  and  having  then  a  valve  only  at  the 
bottom  ? 


GASES. 


Ill 


189.  Experiments  with  the  Condenser.— If  the  reservoir 
be  partially  filled  with  water,  and  a  tube  runs  from  under 
the  surface  of  the  water  into  the  air,  the  water  may  be 
forced  out  by  compressing  air  above  it.     Many  of  the  ex- 
periments with  the  air-pump  may  be  reversed  with  the 
condenser.     A   foot-ball   or    bladder    may   be    shrivelled. 
(How  ?)     A  thin  cube  of  glass  may  be 

crushed.  The  specific  gravity  of  air 
or  any  other  gas  can  be  best  found  by 
compressing  a  considerable  quantity  of 
it  in  a  receiver  and  then  weighing  it. 
(Art.  168.) 

190.  The  Air-Brake.— This  very  use- 
ful invention  consists  of  a  powerful  con- 
"denser  attached  to  a  locomotive,  and 
working  by  steam.    It  is  connected  by 
rubber  tubes  with  a  reservoir  under 
each  car,  and  fills  these  reservoirs  with 
highly-compressed  air.     When  the  en- 
gineer wishes   to   stop   the   train,  he 
moves  a  lever,  which  allows  the  com- 
pressed air  in  the  reservoir  to  rush  into 
a  cylinder,  also  under  the  car,  and,  by 
driving  a  piston  along  this  cylinder, 
it   presses   the   brakes   very   strongly 
against  the  wheels. 

191.  The  Common  Pump,— Fig.  100 
shows  the  common  pump.     It  consists 
of  a  tube  (pump-stock),  in  which  works 

a  piston  having  in  it  a  valve  opening  upward.  Opening 
into  the  bottom  of  this  there  is  a  narrower  tube,  which 
runs  down  into  the  water.  At  the  top  of  this  tube  is 
another  valve,  also  opening  upward.  To  show  how  it 
works,  suppose  that  no  water  is  standing  in  the  pump. 
When  the  piston  moves  up  from  the  bottom  of  the  pump- 
stock  as  its  valve  remains  closed,  it  tends  to  form  a  vacuum 


FIG.  100. — THE  COMMON 
PUMP. 


112  NATURAL   PHILOSOPHY. 

below  it.  The  atmospheric  pressure  upon  the  surface  of  the 
water  in  the  well  drives  up  water,  and  the  air  in  the  tube 
above  it,  to  fill  this  vacuum.  When  the  piston  descends,  the 
lower  valve  falls,  and  keeps  there  the  air  and  water  that 
have  been  drawn  up  from  below,  and  the  valve  in  the  piston 
opens  to  allow  the  piston  to  pass  through  this  air  and  water 
in  the  pump-stock.  The  next  stroke  of  the  piston  raises 
the  air  and  water  above  it  to  the  spout,  and  the  water  rises 
from  the  well  as  before  to  fill  its  place.  And  at  each  suc- 
cessive stroke  the  pump-stock  full  of  water  is  pumped  out. 
If  the  valves  are  tight,  the  tube  and  pump-stock  are  usually  stand- 
ing full  of  water,  so  that  the  latter  begins  to  flow  at  the  first  upward 
stroke. 

192.  Depth  from  which  Water  may  be  raised  by  the  Com- 
mon Pump. — We  have  found  that  the  atmosphere  will  sus* 
tain  a  column  of  mercury  30  inches  high ;  and,  as  mercury 
is  about  13 £  times  as  heavy  as  water,  the  atmosphere  will 
sustain  a  column  of  water  13 }  times  30  inches  high,  or 
about  34  feet.  Since  the  atmospheric  pressure  will  raise 
water  34  feet,  if  a  pump  were  perfectly  made  it  would 
work  as  long  as  the  upper  valve  was  within  that  distance 
from  the  bottom  of  the  well.  Practically,  however,  the 
upper  valve  ought  never  (i.e.,  at  the  upper  end  of  the 
stroke)  to  be  more  than  about  25  or  26  feet  from  the  sur- 
face of  the  water.1  Water  can  be  raised  farther  than  that 
by  having  the  upper  part  of  the  pump-stock  lengthened  so 

1  It  was  through  the  observation  of  this  fact  that  Galileo  (gal-i- 
lee'o)  (great  Italian  astronomer  and  philosopher,  1564-1642)  first  sug- 
gested the  true  cause  of  water  rising  in  a  pump.  It  had  formerly  been 
explained  by  saying  that  nature  abhorred  a  vacuum  and  therefore  the 
water  rose  to  fill  the  vacuum  caused  by  the  piston.  The  Grand  Duke 
of  Tuscany  wished  to  pump  water  from  a  depth  of  40  or  50  feet,  but 
the  pumps  would  not  work.  Galileo  found  that  the  water  would  rise 
but  32  feet,  and  suggested  that  it  was  the  weight  of  the  atmosphere 
that  supported  the  water  at  that  height.  His  pupil  Torricelli  (1608- 
1647)  afterwards  discovered  that  the  atmosphere  would  support  30 
inches  of  mercury,  as  explained  in  Art.  170. 


GASES. 


113 


as  to  bring  the  spout  some  distance  above  the  upper  end 
of  the  stroke  of  the  piston.  The  piston  then  lifts  the 
water  above  it  to  the  spout. 


FIQ.  101.— A  FORCE-PUMP. 


FIG.  102.— MODEL  OF  A 
FORCE  -  PUMP  WITH 
AIR-CHAMBER. 


193.  The  Force-Pump, — To  raise  water  higher  than  26 
feet,  force-pumps  are  often  used.     Fig.  101  represents  a 
simple  kind.     The  piston  is  solid.     The  up-stroke  draws 
the  water  from  the  well  and  fills  the  pump-stock  with  it. 
The  down-stroke  closes  the   lower  valve  and  forces  the 
water  through  the  side-valve  and  up  the  pipe  seen  there. 

194.  Force-Pump  with  Air-Chamber. — Sometimes  force- 
pumps   are   furnished  with  air-chambers  to  cause  a  con- 
tinual flow  of  water.     Fig.  102  shows  a  model  of  such  a 
pump.    The  water  is  forced  up  into  the  tube  which  branches 
off  to  the  left,  and  compresses  the  air  there  into  the  upper 

h  10* 


114 


NATURAL   PHILOSOPHY. 


part.    This  presses  upon  the  surface  of  the  water  and  drives 

it  in  a  constant  stream  through 
the  small  tube. 

195.  Rotary  Pump.— To 
supply  cities  with  water,  to 
empty   mines,  and    wherever 
large  quantities  of  water  must 

\B  be  raised,  rotary  pumps  are 
often  used.  They  are  made 
in  many  ways,  one  being 
shown  in  Fig.  103.  It  is  a 
round  iron  box,  in  which  four 
paddles  turn.  These  suck  the 
water  up  the  lower  tube  and 
drive  it  up  the  upper  one. 

196.  Fire-Engine.— Fig.  104 
represents    a   common    hand 

fire-engine.    It  has  two  force-pumps,  which  drive  the  water 


Fia.  103.— ROTARY  PUMP. 


FIG.  104. — HAND  FIRE-ENGINE. 


into  an  air-chamber  between  them,  whence  it  is  forced  out 
through  the  hose  by  the  pressure  of  the  compressed  air. 


GASES. 


115 


The  water  is  usually  supplied  by  being  carried  in  buckets, 
and  the  pumps  are  worked  by  several  men.  The  steam 
fire-engine  is  a  powerful  steam-pump,  generally  rotary, 
which  draws  its  water  through  a  hose  from  some  artificial 
or  natural  reservoir,  and  drives  it  out  with  great  force 
through  another  hose. 

197.  The  Siphon. — If  a  tube  open  at  both  ends  be  bent, 
as  in  Fig.  105,  having  one  arm  longer  than  the  other,  we 
have  a  siphon.  If  this  be  filled  with  water,  and  then  be 
placed,  as  in  the  figure,  with  the  short  arm  in  a  vessel  of 


FIG.  105.— A  SIPHON. 

water,  the  water  in  the  tube  will,  of  course,  tend  through 
gravity  to  flow  down,  and  out  of,  both  arms  of  the  tube ; 
but  this  it  cannot  do,  because  it  would  leave  a  vacuum 
above.  And  as  the  long  column,  ef,  is  heavier  than  the 
short  one,  dc,  the  water  runs  down  the  long  arm,  and  that 
in  the  vessel  flows  up  the  short  arm  (through  the  pressure 


116 


NATURAL   PHILOSOPHY. 


of  the  air  upon  the  water  in  the  vessel)  to  fill  the  vacuum 
there,  and  in  this  way  the  vessel  may  be  emptied  of  the 
water. 

198.  Starting  the  Siphon. — It  is  evident  that  the  siphon 
will  not  start  itself.  It  may  be  filled  by  putting  it  under 
water,  and  then  both  ends  must  be  closed  by  the  fingers 


FIG.  106.— A  SIPHON  WITH  EXHAUST-TUBE. 

until  it  is  in  position.  Or  it  may  be  put  in  position  empty 
and  filled  by  sucking  at  the  end  of  the  long  arm.  Where 
this  cannot  be  done,  or  is  undesirable,  the  siphon  can  have 
a  suction-branch,  as  in  Fig.  106. 

Why  is  the  end  of  the  siphon  kept  closed  by  the  finger  in  starting 
it  ?  Will  it  be  necessary  to  suck  the  long  arm  full  before  the  siphon 
will  begin  to  run  ? 

199.  Uses  and  Limitations  of  the  Siphon.— The  siphon  is  often 

used  to  empty  vessels  of  liquids.  It  may  be  used  to  carry  the  water 
from  a  spring  over  a  low  hill  to  a  house  or  a  barn  which  is  below  the 
level  of  the  spring. 

The  end  of  the  tube  from  which  the  liquid  flows  must  always  be 
below  the  surface  of  the  liquid  in  the  vessel.  If  the  surface  should 


GASES. 


117 


be  lowered  until  it  is  on  the  same  level  with  the  outlet,  the  flow 
will  stop.     As  atmospheric  pressure  will  not  raise  water  more  than 


FIG.  107. 


FIG.  108.— TANTALUS'S 
CUP. 


34  feet,  if  water  is  to  be  siphoned,  the  top 
of  the  curve  must  not  be  more  than  34 
feet  higher  than  the  surface  of  the  water. 

200.  Experiments  with  the  Siphon. 

— Experiment  51. — Fig.  107  represents 
a  vessel  with  a  closely-fitting  lid  which 
has  two  openings  in  it.  Through  a  cork 
fitting  one  of  these  openings  runs  a 
siphon-tube.  After  being  started,  the 
water  in  the  vessel  will  flow,  but  will 
stop  when  the  other  opening  in  the  lid 
is  stopped  by  the  finger  :  why  ? 

Experiment  52. — Fig.  108  represents 
the  "cup  of  Tantalus."  It  will  be  noticed 
that  the  handle  is  a  siphon,  the  short  arm 
of  which  opens  into  the  bottom  of  the 
cup.  When  the  cup  is  filled  full,  or 
when  it  is  tilted  so  as  to  bring  the  water 
up  to  the  highest  part  of  the  handle,  the 
water  will  begin  to  run,  and  will  empty 
the  cup. 

Fig.  109  shows  how  a  self-acting  foun- 
tain can  be  made  of  the  bottom  of  a 
glass  bottle,  a  cork,  and  two  glass  tubes. 
A  dandelion-stem  will  make  a  good 
siphon.  Try  it. 


FIG.  109.— SELF-ACTING  FOUNTAIN. 


201.  Intermittent  Springs. — These  are  springs  which  flow 
only  at  intervals.  They  have  been  explained  on  the  prin- 
ciple of  the  siphon.  Fig.  110  shows  how  this  may  be.  If 
a  reservoir  in  the  earth  had  such  a  siphon-shaped  outlet  as 
is  there  shown,  when  it  filled  up  to  the  bend  of  the  outlet^ 


118 


NATURAL   PHILOSOPHY. 


the  water  would  run  until  the  reservoir  was  emptied,  and 
then  would  cease  running  until  filled  up  to  the  bend  again. 

% ~. — ~  "91 


FIG.  110. — THE  INTERMITTENT  SPRING. 

Exercises. — 1.  In  Fig.  82  the  mercury  stands  90  inches  higher  in 
the  long  tube  than  in  the  short  one.  If  ab  equals  6  inches,  how 
many  inches  of  air  are  there  below  bl  Ans.  1^  inches. 

2.  How  many  inches  of  mercury  have  been  poured  in  to  condense 
this  ?     Ans.  99  inches. 

3.  If  one  column  is  20  inches  higher  than  the  other,  what  is  the 
length  of  the  air-column  in  the  short  arm  ?     Since  the  pressure  is  If, 
or  f  as  great  as  before,  the  air  will  occupy  f  as  much  space,  or  3f 
inches. 

4.  If  one  column  is  10  inches  higher  than  the  other,  what  is  the 
length  of  the  air-column  in  the  short  arm  ?     Ans.  4^  inches.     What 
if  it  is  45  inches  higher  ? 

5.  The  specific  gravity  of  mercury  is  13.6,  that  of  alcohol  is  .8  :  how 
high  a  column  of  alcohol  will  the  atmosphere  support?     Ans.  42  feet 
6  inches. 

6.  How  high  a  column  of  sulphuric  acid,  whose  specific  gravity  is 
1.8,  will  the  atmosphere  support  ? 

7.  A  tumbler  whose  sides  are  vertical  is  inverted  and  pushed  down, 
into  water   until  the  air  is   condensed  into  the  upper  half  of  the 


GASES.  H9 


tumbler  :  how  deep  is  the  tumbler  ?    Ans.  34  feet.     Is  it  the  bottom, 
the  middle,  or  the  top  of  the  tumbler  that  is  34  feet  deep? 

8.  How  deep  must  the  tumbler  be  if  the  air  is  compressed  into  the 
upper  third  of  it  ?     Ans.  68  feet.     How  deep  if  it  is  compressed  into 
the  upper  fifth  of  the  tumbler  ? 

9.  How  high  will  the  barometer  stand  at  a  place  1800  feet  above 
the  sea  ? 

10.  Barometers  are  often  marked  FAIR  opposite  30J  inches,  CHANGE 
opposite  29J  inches,  RAIN  opposite  28J  inches,  etc.     If  a  person  were 
to  buy  such  a  barometer  and  take  it  to  a  place  900  feet  above  sea- 
level,  what  would  be  the  result?  what  if  he  lived  in  a  place  1800  or 
2700  feet  above  the  sea  ? 

11.  Explain  how  you  fill  your  lungs  with  air. 

12.  How  do  you  suck  water  through  a  tube? 

13.  Why  will  a  liquid  flow  out  of  the  spigot  of  a  barrel  so  much 
faster  when  the  bung  at  the  top  is  out  ? 

14.  Why  does  water  gurgle  and  flow  so  irregularly  when  poured 
out  of  a  bottle  ? 

15.  Why  will  water  flow  through  a  funnel  so  much  better  when 
the  funnel  is  raised  a  little  in  the  mouth  of  the  bottle  which  you  are 
filling  with  water? 

16.  What  part  of  the  air  is  left  in  the  receiver  of  an  air-pump 
when  the  mercury  in  the  gauge  is  3  inches  higher  on  one  side  than  on 
the  other  ?     Ans.  TV     When  £  inch  higher  ? 

17.  What  is  the  difference  of  heights  in  the  gauge  when  j^^  of 
the  air  is  left  in  the  receiver  ? 

18.  A   pair  of  Magdeburg  hemispheres   have    a  diameter   of   3 
inches.     If  the  air  were  perfectly  exhausted,  what  force  would  it 
take  to  pull  them  apart  ?     Ans.  106  pounds. 

19.  Otto  Guericke's  hemispheres  are  said  to  have  been  2  feet  in  di- 
ameter.    Had  he  been  able  to  exhaust  all  the  air,  what  force  would 
have  been  needed  to  pull  them  apart?     It  is  sometimes  said  that 
30  horses,  15  on  each  side,  were  unable  to  pull  them  apart.     Can  that 
be  true  ? 

20.  If  the  inside   diameter  of  a  weight-lifter   is   6   inches,  what 
weight  will  it  lift,  provided  a  perfect  vacuum  be  produced  ? 

21.  How  heavy  a  stone  will  a  perfect  u  sucker,"  4  inches  in  diame- 
ter, lift  ? 

22.  What  is  the  difference  in  the  heights  of  the  columns  of  the 
air-pump  gauge  when,  by  using  Sprengel's  pump,  only  T.-jnrV.oinr  of 
the  air  is  left  in  the  receiver  ?     Ans.  .00003  inch. 

23.  Bunsen's  air-pump  uses  falling  water  as  Sprengel's  does  falling 
mercury :  how  long  must  the  tube  below  x  be  ? 

24.  Denver,  Col.,  is  about  1  mile  above  sea-level :  how  high  would  a 
perfect  pump  raise  water  there?   Ans.  28  feet.     (See  foot-note,  p.  98.) 

25.  If  a  certain  pump  will  raise  fresh  water  25  feet,  how  high  will 
it  raise  salt  water  ? 

26.  The  diameter  of  the  piston  of  a  pump  is  2   inches,  and  the 
height  of  the  top  of  the  water  in  the  pump  above  the  piston  is  18 
feet :  what  is  the  pressure  upon  the  piston  ? 

27.  What  will  be  the  pressure  upon  the  piston  in  the  last  problem  if 
the  diameter  of  the  upper  10  feet  of  the  column  of  water  is  3  inches  ? 


120  NATURAL  PHILOSOPHY. 


CHAPTEE    T. 

SOUND. 
SECTION  I.— THE  CAUSE  AND  PHENOMENA  OF  SOUND. 

202.  Sound  is  a  Vibration. — All  sound  is  caused  by  the 
vibration  of  some  body.  When  a  violin-string  is  sounded, 
the  vibrations  can  be  seen.  If  a  tuning-fork  be  sounded, 
and  the  fork  be  touched  to  the  lips  or  teeth,  the  vibrations 
can  be  felt. 

Experiment  53. — Fasten,  with  wax,  a  short  bit  of  fine  wire,  or  a 
bristle,  to  the  end  of  one  prong  of  a  tuning-fork.  Sound  it  by  striking 
it  against  the  table,  and  draw  the  end  of  "the  wire  gently  over  a  piece 
of  smoked  glass.  The  vibrations  of  the  fork  will  trace  a  beautiful 
wavy  line  on  the  glass. 


FIG.  111.— TUNING-FORK  RECORDING  ITS  VIBRATIONS. 

The  word  sound  is  used  in  two  senses.  It  is  sometimes  used  to  de- 
note the  vibration  of  the  sounding  body,  but  is  often er  used  to  denote 
the  effect  of  this  vibration  upon  an  organ  of  hearing.  Accordingly, 
when  the  old  question,  "If  a  tree  were  to  fall  in  a  forest  fifty  miles 
from  any  living  being,  would  there  be  any  sound?"  is  asked,  the 
answer  depends  upon  which  definition  of  sound  is  taken. 

203.  Sound  usually  brought  to  the  Ear  by  Vibrations  of 
the  Air. — As  sound  is  always  caused  by  the  vibrations  of 
some  body  at  a  distance  from  the  ear,  there  must  be  some 
way  by  which  it  is  carried  to  the  ear.  This  is  almost 


SOUND. 


121 


always  done  by  vibrations  of  the  air,  as  may  be  shown  by 
the  following  experiment. 

Experiment  54.  —  Set  a  small 
clock,  or  a  music-box,  under  the  re- 
ceiver of  an  air-pump,  taking  care 
to  put  under  the  clock  a  number  of 
thicknesses  of  flannel.  Exhaust  the 
air,  and  the  ticking  of  the  clock,  or 
the  sound  of  the  music-box,  will 
grow  fainter  and  fainter,  until  it  can 
no  longer  be  heard. 

Fig.  112  shows  a  bell  which  can 
be  kept  ringing  by  clock-work,  and 
is  hung  by  cords  in  the  receiver  of 
an  air-pump,  which  is  often  used  to 
prove  this  fact.  Here,  as  also  above, 
the  experiment  is  more  satisfactory 
if,  after  the  air  is  exhausted  as  far 
as  possible,  the  receiver  be  filled  with 
hydrogen  and  again  pumped  out. 
Fig.  113  is  a  simpler  piece  of  appa- 
ratus to  illustrate  the  same  thing. 

On  the  tops  of  high  mountains 
sounds  are  considerably  fainter  than 
upon  the  surface  of  the  earth  :  why  ? 


I 
FIG.  112.— BELL  IN  A  VACUUM. 


204.  How  Air  conveys  Sound. — Suppose  a  tuning-fork  be 
sounded  and  held  at  one  end  of  a  tube, 
as  shown  in  Fig.  114.  As  the  prong  of 
the  fork  flies  out,  it  will  drive  the  air  that 
is  in  front  of  it  forward  a  little  way  and 
compress  it.  This  air  will  condense  and 
drive  forward  the  air  in  front  of  it,  and 
so  the  condensation  will  be  driven  through 
the  tube.  Any  one  particle  of  air  moves 
forward  only  a  very  little  way,  when  it  gives 
its  motion  to  the  particle  ahead  of  it,  but  the 
condensation,  or  the  wave,  moves  through  the  whole  tube.  Sound- 
waves are  just  like  water-waves,  as  described  in  Art.  158, 
except  that  in  sound-waves  the  particles  of  air  move 
F  11 


FIG.  113.— BELL  IN  A 
VACUUM. 


122 


NATURAL  PHILOSOPHY. 


lengthwise,  but  in  water-waves  the  particles  of  water  move 
up  and  down. 


FIG.  114.— SOUND-WAVES  IN  A  TUBE. 

The  sound-wave  is  not  a  puff  or  blast  of  air,  such  as  you  blow 
from  your  mouth.  Tyndall1  has  shown  this  very  neatly  by  the  fol- 
lowing experiment. 

Experiment  55. — Fill  the  long  tube  shown  in  the  figure  with  smoke 
from  burning  paper,  set  a  lighted  candle  at  one  end,  and  make  a  loud 
noise,  by  clapping  two  blocks  together,  or  otherwise,  at  the  other  end. 
The  flame  will  be  put  out,  yet  no  blast  of  air  rushes  through  the 
tube,  for  the  smoke  has  not  been  driven  out. 


FIG  115. 

•  In  the  open  air  these  condensations  move  in  all  direc- 
tions. Each  one  must  therefore  be  a  spherical  shell,  grow- 
ing larger  as  it  moves  farther  in  every  direction  from  where 
the  sound  was  made.  Following  every  condensation  there 
must  of  course  be  a  rarefaction.  And  so  these  successive 
waves  of  condensation  and  rarefaction  are  constantly  given 
out  in  all  directions  as  long  as  the  sounding  body  vibrates. 

1  John  Tyndall  (1820-),  an  English  natural  philosopher,  and  one 
of  the  greatest  of  living  scientists.  "  Tyndall  on  Sound"  is  the  best 
book  on  this  subject  in  the  English  language  for  most  readers  and 
students. 


SOUND.  123 


205.  Velocity  of  Sound  in  the  Air. — Every  one  who  uses 
this  book  has  probably  noticed  that  when  a  whistle,  some 
distance  off,  is  blown,  the  escaping  steam  can  be  seen  a 
little  time  before  the  sound  can   be  heard,  and  that  the 
sound  keeps  coming  just  as  long  after  the  steam  can  be  seen 
to  have  stopped.     And  when  a  wood-chopper  is  working  at 
a  considerable  distance,  you  hear  the  blow  after  you  see 
it.   As  we  shall  presently  learn,  light  travels  so  exceedingly 
fast  that  we  see  the  steam  immediately  after  it  escapes,  so 
that  the  difference  between  the  times  of  seeing  it  and  hear- 
ing the  whistle  is  the  time  that  it  has  taken  the  sound  to 
travel  from  the  whistle  to  us. 

The  velocity  of  sound  through  the  air  has  been  very 
carefully  measured.  It  is  found  to  vary  according  to  the 
temperature.  When  the  temperature  of  air  is  at  the 
freezing-point  of  water,  32  degrees  in  our  common  ther- 
mometers (Fahrenheit's),  sound  travels  through  it  1090 
feet  per  second.  And  its  speed  is  about  1  foot  more  per 
second  for  every  degree  that  the  thermometer  is  above  32°. 

How  fast  does  sound  travel  through  the  air  when  the  temperature 
is  70°  ? 

206.  Solids  and  Liquids  may  also  convey  Sound. 

Experiment  56. — Get  a  companion  to  scratch  one  end  of  a  long 
piece  of  wood  (a  board  in  the  floor  or  a  sound  fence-rail  will  do) 
lightly  with  a  pin.  By  putting  your  ear  to  the  other  end 
you  can  hear  the  scratch  distinctly,  although  you  cannot 
hear  it  through  the  air  when  you  lift  your  ear  from  the 
wood.  Try  the  same  thing  with  a  long  bar  of  iron. 

Experiment  57. — Get  a  companion  to  strike  two  stones 
together  10  feet  from  you,  and  notice  how  loud  it  sounds. 
Hold  your  head,  or  one  ear,  under  water  while  he  strikes 
the  stones  together  under  the  water,  at  the  same  distance, 
and  notice  how  much  louder  it  sounds. 

Sound  travels  faster  and  farther  through  solids  and  liquids 
than  through  the  air.     Through  iron  it  travels  about  16,000    FIG.  116.— 
feet  per  second,  through  most  kinds  of  wood  almost  as  fast,       scope!0" 
and  through  water  about  5000  feet  per  second.     The  stetho- 
scope is  a  small  tube  of  wood  or  metal  widening  out  at  one  end,  whic'n 
is  much  used  by  physicians.    The  physician  places  the  wide  end  upon 


124  NATURAL   PHILOSOPHY. 

his  patient's  chest,  and  puts  his  ear  to  the  other  end.  The  faint  sounds 
made  by  the  organs  in  the  chest  are  distinctly  carried  to  his  ear 
through  the  stethoscope,  and  he  can  judge  of  their  condition.  The 
Indians  are  said  to  put  their  ears  to  the  ground  and  thus  hear  the  ap- 
proach of  their  enemies  long  before  it  could  be  heard  through  the  air. 
The  ordinary  string  telephone  which  boys  make  by  knocking  the 
bottoms  out  of  two  fruit-cans,  stretching  parchment  tightly  over  one 
end  of  each,  and  joining  these  parchments  with  a  stretched  string, 
will  convey  sound  quite  a  distance.  A  whisper  in  one  can  easily  be 
heard  in  the  other  across  the  street.  And  when  carefully  made  and 
very  fine  copper  wire  is  used  instead  of  string,  conversation  can  be 
carried  on  through  them  for  a  quarter  of  a  mile  or  farther. 

Experiment  58. — Suspend  a  poker  by  two  strings,  and  thrust  the 
fingers  holding  the  poker  into  your  ears.  Then  swing  the  poker 
against  a  piece  of  wood,  and  you  will  be  surprised  at  the  sound. 

207.  Loudness  of  Sound, — Tap  a  table  gently,  and  a  faint 
sound  is  produced  ;  strike  it  hard,  and  a  loud  sound  is  pro- 
duced ;  or,  better,  pull  a  violin-string  a  very  little  to  one 
side,  and  it  sounds  faintly  ;  pull  it  strongly  to  one  side,  and 
it  sounds  loud.     Short  vibrations  of  the  sounding  body  pro- 
duce faint  sounds,  long  vibrations  produce  loud  ones.     Short 
vibrations  of  the  sounding  body  make  short  vibrations  of 
the  particles  of  air,  and  longer  vibrations  of  the  body  make 
longer  vibrations  of  the  particles  of  air.     Hence  although 
each  particle  of  air  in  a  sound-wave  moves  only  a  very  short 
distance  forward   and  backward,  yet  it  makes  a  longer 
swing  when  conveying  a  loud  sound  than  when  conveying 
a  faint  one. 

208.  Loudness  of  Sound  affected  by  Distance. — Common 
experience  teaches  us  that  all  sounds  grow  fainter  as  they 
get  farther  from  the  sounding  body,  and  finally  become  too 
faint  to  be  heard.     But  if,  instead  of  being   allowed   to 
spread  in  every  direction,  the  sound  be  confined  to  a  narrow 
tube,  it  is  carried  much  farther.     Hence  speaking-tubes  are 
often  found  in  large  buildings  so  arranged  that  a  whisper 
into  one  end  of  the  tube  can  be  heard  at  the  other  end  in  the 
farthest  corner  of  the  building.    Speaking-trumpets  are  much 
used  at  sea  to  enable  the  voice  of  the  officer  in  command 


SOUND.  125 


to  be  heard  better  and  farther  in  any  one  direction.     They 
seem  to  guide  the  sound  of  the  voice  in  one  direction,  so 


FIG.  117.— SPEAKING-TRUMPET. 

that  it  is  louder  and  goes  farther  than  if  allowed  to  spread. 
Ear-trumpets  are  funnel-shaped  instruments  that 
collect  all  the  sound  that  enters  the  mouth  of  the 
funnel  and  concentrate  it  into  a  small  opening  at 
the  other  end  of  the  ear-trumpet.  By  putting 
the  small  end  to  the  ear,  partially  deaf  persons 
can  hear  better. 

If  sound  moves  through  the  air  unobstructed  in  all  di- 
rections, and  if  the  air  is  uniform,  or  homogeneous,  the 
loudness  must  vary  inversely  as  the  square  of  the  distance 
from  the  sounding  body.  Twice  as  far  off  the  sound  would 
be  .one-fourth  as  loud,  tbree  times  as  far  off  one-ninth  as 
loud,  etc.  This  is  because  at  twice  the  distance  from  the 
sounding  body  the  air  in  a  hollow  shell  or  surface  of  a  sphere  of  twice 
the  former  radius  is  vibrating.  But  surfaces  of  spheres  increase  ac- 
cording to  the  squares  of  the  radii ;  therefore  the  sound  is  spread  out 
over  four  times  as  much  surface,  and  must  be  one-fourth  as  loud  at 
any  one  place. 

209.  Conditions  of  the  Atmosphere  as  affecting  Sound.— 

Although  sound  travels  many  times  faster  than  the 
strongest  wind,  yet  it  can  often  be  heard  three  or  four 
times  as  far  with  the  wind  as  against  it.  The  cause  is  not 
certainly  known. 

It  was  formerly  thought  that  rain,  snow,  fog,  etc.,  ob- 
structed sound  ;  but  Tyndall  has  recently  shown  that  they 
have  no  effect  whatever  upon  the  transmission  of  sound. 
The  same  observer  has  shown  the  existence  of  acoustic 
clouds  in  the  atmosphere.  These  are  masses  of  air  differing 
from  the  surrounding  air  in  temperature,  or  in  the  amount  of 

11* 


126  NATURAL   PHILOSOPHY. 

moisture  they  contain.  .  They  have  no  connection  with  or- 
dinary clouds,  they  are  entirely  invisible,  and  the  air  may 
be  full  of  them  upon  the  clearest  day.  Yet  they  obstruct 
and  reflect  sound  very  much.  It  is  to  the  reflections  from 
these  acoustic  clouds  that  the  rolling  of  thunder  seems  to 
be  mainly  due.  And  probably  the  fact  that  noises  are  heard 
farther  and  more  distinctly  by  night  than  by  day  is  partly 
due  to  there  being  fewer  acoustic  clouds  formed  by  night 
than  by  day,  and  partly  also  to  the  stillness  of  the  night.1 

210.  Reflection  of  Sound. — When  sound-waves  strike  a 
wall  or  other  obstruction,  they  rebound  or  are  reflected, 
and  the  angle  of  reflection  is  equal  to  the  angle  of  inci- 
dence. 

Fig.  119  illustrates  an  experiment  in  the  reflection  of  sound.  Two 
concave  metal  mirrors  are  placed  facing  each  other  and  so  far  apart 
that  the  ticking  of  a  watch  could  not  be  heard  from  one  to  the  other. 
Then,  as  shown  in  the  figure,  a  watch  is  hung  in  front  of  one  so  that 
the  sound-vibrations  are  reflected  out  from  the  mirror  in  a  straight 
line  to  the  other  one,  which  concentrates  them  so  that  if  the  ear  is 
placed  there,  or  if  a  short  speaking-tube  runs  from  there  to  the  ear, 
the  ticking  of  the  watch  can  be  distinctly  heard. 

211.  Whispering-Galleries. — In  some  large  circular  build- 
ings it  is  found  that  low  whispers  spoken  near  the  wall  on 
one  side  of  the  building  can  be  heard  distinctly  at  the  op- 
posite side.     The  sound  seems  to  be  reflected  repeatedly 
until  it  reaches  the  opposite  side,  when  it  is  so  concen- 
trated from  all  directions  that  it  is  distinctly  heard.     The 
gallery  in  the  dome  of  St.  Paul's  Cathedral  in  London  is  a 
famous  whispering-gallery.     The  dome  in  the  Capitol  at 
Washington  is  another. 

212.  Echoes. — When  the  reflecting  surface  is  near  the 
source  of  the  sound,  as  the  walls  of  an  ordinary  room  in 

1  The  writer's  own  observations  leave  no  doubt  in  his  mind  that 
the  popular  notion  that  distant  sounds  can  be  heard  more  distinctly 
before  a  storm  is  correct.  Probably  at  such  a  time  the  air  is  homo- 
geneous and  free  from  these  acoustic  clouds  ;  but  some  instances  are 
not  easily  explained  in  this  way. 


SOUND. 


127 


which  a  sound  is  made,  the  reflection  follows  the  sound 
itself  so  closely  that  it  cannot  be  distinguished  from  it.    It 


FIG.  119.— CONCENTRATION  OF  REFLECTED  SOUND. 

may,  however,  modify  one's  voice  in  some  way  and  give  a 
peculiar  resonance  to  the  room.     But  when  the  reflecting 


FIG.  120. — REFRACTION  OF  SOUND. 


surface  is  fifty  feet  or  more  away,  the  reflection  can  be  heard 
after  the  sound  ceases,  and  is  called  an  echo. 


128  NATURAL   PHILOSOPHY. 

Between  two  walls,  or  between  cliffs,  and  in  like  places,  echoes  are 
often  repeated  many  times  by  being  reflected  from  side  to  side.  Large 
halls  sometimes  have  an  echo  that  is  very  annoying  to  both  the  speaker 
and  his  hearers.  In  such  cases  the  echo  is  generally  less  when  the 
hall  is  filled  with  people,  and  especially  so  if  the  seats  rise  towards 
the  back  of  the  hall,  or  if  there  is  a  gallery  there. 

213.  Refraction  of  Sound. — Fig.  120  shows  how  a  faint 
sound  may  be  concentrated  so  as  to  be  heard  farther  oif 
than  it  could  otherwise  be  heard.  B  is  a  small  balloon  filled 
with  some  gas  heavier  than  air,  as  carbonic  acid.  The  waves 
of  sound  are  bent  around,  or  refracted,  by  the  heavy  gas 
and  concentrated  at  one  point.  If  the  ear  is  placed  there, 
or  if  a  funnel  is  placed  there  to  convey  the  sound  to  the 
ear,  the  ticking  of  the  watch  may  be  distinctly  heard.  This 
refraction  of  sound  is  like  the  concentration  of  the  sun's 
heat  with  a  burning-glass.  In  light  it  is  a  very  important 
subject,  and  will  be  fully  taken  up  there. 


FIG.  121. — EDISON'S  PHONOGRAPH. 

214.  The  Phonograph. — Fig.  121  represents  a  phonograph,  a  re- 
markable talking-machine  recently  invented  by  Mr.  Edison.1  4  is  a 
brass  cylinder  into  which  is  cut  a  continuous  groove,  winding  around 
it  from  one  end  to  the  other.  When  the  handle  1  is  turned,  the  screw- 
thread,  seen  under  7,  moves  the  cylinder  slowly  along  to  the  left 

1  Thomas  A.  Edison  (1847-),  a  famous  American  inventor,  who 
lives  at  Menlo  Park,  New  Jersey. 


SOUND.  129 


while  it  is  revolving.  Above  4  is  the  mouth-piece,  the  bottom  of 
which  is  covered  with  a  thin  elastic  metal  plate.  From  the  under 
side  of  this  plate  a  short  needle  runs  down.  To  use  the  phonograph, 
a  piece  of  tin-foil  is  wrapped  tightly  around  the  brass  cylinder,  and  the 
handle  6  is  pushed  down  upon  the  screw-head  5  and  held  there.  This 
presses  the  needle  down  upon  the  tin-foil.  If  the  handle  is  turned  as 
the  cylinder  ^revolves  and  moves  to  the  left  at  the  same  time,  the 
needle  pushes  the  tin-foil  down  into  the  groove  beneath  it,  and  thus 
makes  a  shallow  spiral  groove  in  the  tin-foil.  But  if  you  talk  into 
the  mouth-piece  the  sound-waves  will  make  the  elastic  plate  vibrate, 
and  the  needle,  being  attached  to  it,  will  also  vibrate  up  and  down, 
and  will  make  successive  dots  and  dashes  in  the  bottom  of  the  groove 
in  the  tin-foil.  If  we  were  to  take  the  tin-foil  off  the  cylinder  and 
examine  the  bottom  of  the  groove  with  a  microscope,  we  should  find 
a  peculiar  indentation  for  every  pulse  of  the  sound-wave.  But,  in- 
stead of  taking  the  foil  off  the  cylinder,  let  us  raise  6  and  run  the 
cylinder  back  to  the  starting-place.  If  the  needle  be  now  pressed 
down  into  the  groove  and  the  handle  be  turned  as  it  was  when  we 
were  talking  to  it,  the  indentations  there  will  cause  the  needle  to 
vibrate  up  and  down,  precisely  as  it  vibrated  when  it  caused  these 
indentations,  and  the  needle  will  vibrate  the  plate,  just  as  the  plate  at 
first  vibrated  the  needle,  and  hence  cause  it  to  send  out  into  the  air 
the  same  vibrations  or  sounds  as  were  driven  against  it  when  you 
talked  to  it.  In  this  way  the  phonograph  repeats  the  words  said  to  it, 
as  well  as  laughter,  crying,  and  sounds  of  any  kind.  But,  as  its  voice 
is  feebler  than  yours,  it  needs  for  a  speaking-trumpet  a  cone  of  paper, 
in  order  that  it  may  be  heard  over  a  large  room. 

SECTION  II.-MUSICAL  SOUND. 

215.  Noise  and  Musical  Sound. — When  the  sound-vibra- 
tions are  irregular,  no  two  at  the  same  distance  apart,  we 
hear  a  noise,  such  as  would  be  made  by  the  crash  of  a  pane 
of  glass.  But  if  the  waves  of  sound  follow  one  another  at 
regular  intervals,  we  hear  a  musical  sound,  such  as  is  made 
by  the  prong  of  a  tuning-fork  or  a  violin-string,  which  vi- 
brates regularly,  and  produces  sound-waves  all  at  the  same 
distance  apart.  No  matter  how  the  vibrations  are  caused, 
if  they  are  at  regular  intervals  and  rapid  enough,  they  will 
produce  a  musical  sound.  Taps  on  a  table,  the  striking  of 
a  stick  upon  the  pales  of  a  fence  or  the  teeth  of  a  wheel, 


130  NATURAL  PHILOSOPHY. 


the  puffs  of  a  locomotive,  if  regular  and  rapid  enough  to 
blend  together,  .produce  a  sound  as  truly  musical  as  the 
voice  of  the  best  singer,  or  a  note  of  a  flute,  though  it 
may  not  be  as  pleasant. 

If  a  number  of  boys  should  run  across  a  room  all  keeping  step,  the 
noise  of  their  steps  would  be  heard  at  regular  intervals  ;  and  if  they 
could  run  so  fast  that  the  sounds  from  their  steps  would  blend  into 
one  continuous  sound,  they  would  make  a  musical  note.  But  if  the 
same  boys  were  to  run  back  just  as  fast  without  keeping  step,  their 
steps  would  make  a  noise. 

216.  Pitch  of  Sounds. — Experiment  59.— Kun  the  back  of  a 
knife  over  the  milled  edge1  of  a  coin.     You  will  produce  a  musical 
sound.     Eun  the  knife  over  the  edge  faster,  and  your  sound  will  be 
higher ;  run  it  still  faster,  and  the  pitch  will  be  still  higher. 

Experiment  60. — Wind  a  string  around  the  axis  of  the  wheel  (Fig. 
122),  and  pull  it  so  as  to  revolve  the  wheel  rapidly. 
Hold  a  card  to  the  teeth,  and  a  musical  sound  is  pro- 
duced. Revolve  the  wheel  faster  and  faster,  the  pitch 
becomes  higher  and  higher. 

These  experiments  show  that  the  pitch  of 
sounds  depends  upon  the  rapidity  of  the  vibra- 
tions. Their  loudness  depends,  as  has  been 
said,  upon  the  extent  of  the  vibration  of  the 
sounding  body,  and,  therefore,  of  the  parti- 
cles of  air;  their  character,  such  as  distin- 
guishes the  sound  of  a  violin  from  that  of  a  piano  or  a 
human  voice,  is  due  to  other  causes ;  but  the  pitch  of 
sounds  is  due  solely  to  the  number  of  vibrations  per 
second. 

217.  The  Siren. — The  number  of  vibrations  which  pro- 
duce any  given  pitch  of  sound  is  best  found  by  means  of  a 
piece  of  apparatus  called  a  siren,  which  makes  a  musical 
sound  by  a  succession  of  puffs  of  air  following  one  another 

1  If  you  notice,  you  will  see  that  all  the  gold  and  silver  coins  now 
made  in  the  United  States  have  their  edges  finely  notched.  They  are 
said  to  be  milled.  Perhaps  you  can  think  or  find  out  why  they  are 
so  made. 


SOUND. 


131 


very  quickly.  Fig.  124  shows  a  siren  cut  open,  so  that  its 
mechanism  may  be  understood.  Air  is  forced  up  through 
the  tube  below  from  a  pair  of  bellows  (not  shown  in  the 
figure)  into  the  air-chamber  seen  open.  Leading  up  from 
this  is  a  small  opening,  and  above  is  a  wheel  made  to  re- 
volve, and  having  a  circle  of  holes  in  it.  When  one  of  the 
holes  in  the  wheel  comes  over  the  hole  in  the  top  of  the 
air-chamber,  the  air  forced  in  by  the  bellows  can  puff  out; 


FIG.  123.— THE  SIREN. 


FIG.  124. — THE  SIREN, — INSIDE  VIEW. 


when  the  solid  part  of  the  wheel  is  there,  it  cannot.  So,  as 
the  wheel  turns,  a  succession  of  puffs  is  heard  as  the  holes 
in  the  wheel  pass,  one  after  another,  over  the  hole  leading 
up  from  the  air-chamber.  If  the  wheel  turns  fast  enough, 
the  separate  puffs  cannot  be  distinguished  from  one  another, 
but  are  blended  into  one  sound,  rising  higher  in  pitch  as 
the  wheel  goes  faster  and  therefore  produces  more  puffs 
per  second.  By  means  of  the  cog-wheels  seen  at  the  top 
of  the  figure  the  wheel  registers  its  revolutions,  and  the 


132  NATURAL   PHILOSOPHY 

hands  on  the  dials  (Fig.  123)  show  how  many  revolutions 
the  wheel  makes  per  second.  This  multiplied  by  the  num- 
ber of  holes  in  the  wheel  gives  the  number  of  puffs,  and 
therefore  the  number  of  sound-waves  or  vibrations,  per 
second.  It  will  be  noticed  in  Fig.  124  that  the  opening1 
leading  upward  from  the  air-chamber  slants.  This  forces 
the  air  obliquely  against  the  wheel  and  causes  it  to  revolve. 

This  ingenious  little  instrument  will  produce  a  note  of 
any  pitch,  from  the  lowest  to  the  highest,  and  tell  us  the 
number  of  vibrations  it  makes  to  produce  it.  And  if  a  note 
be  sounded  on  any  musical  instrument,  the  pitch  of  the 
siren  may  be  raised  (by  working  the  bellows  harder)  until 
our  ears  tell  us  that  its  pitch  is  the  same  as  that  of  the 
musical  instrument;  then  the  number  of  vibrations  per 
second  of  the  siren  is  the  number  that  the  instrument  is 
making.  In  this  way  we  can  count  the  vibrations  which 
the  human  voice,  or  any  other  musical  sound  of  any  pitch, 
is  producing. 

218.  The  Limits  of  Human  Hearing, — It  is  found  that 
when  the  puifs  of  the  siren  are  fewer  than  16  per  second 
they  are  heard  as  separate  puifs,  but  when  they  reach 
about  that  number  they  cannot  be  separately  heard,  and 
make  a  continuous  and  very  low  note.  The  lower  limit 
of  sounds,  then,  is  about  16  vibrations  per  second,  which 
make  a  sound  of  the  lowest  possible  pitch.  When  the 
puifs  reach  about  38,000  per  second  their  exceedingly 
shrill  piercing  note  suddenly  ceases,  and  though  the  wheel 
can  be  seen  to  be  revolving,  and,  as  the  hands  show,  faster 
than  ever,  nothing  can  be  heard.  We  have  reached  the 
upper  limit  of  human  hearing.  The  ear  can  hear  nothing 
when  the  vibrations  are  more  than  about  38,000  per  second. 

1  There  is  really  a  circle  of  holes  in  the  top  of  the  air-chamber,  cor- 
responding exactly  with  the  holes  in  the  wheel,  and  when  the  air 
puifs  through  one  hole  it  puffs  through  all.  Only  one  puff  is  heard, 
but  it  is  stronger,  and  the  wheel  can  be  driven  around  much  faster, 
than  if  there  were  but  one  upward  opening. 


SOUND.  133 


The  pitch  of  the  keys  of  our  ordinary  pianos  ranges  from  27  to  3482 
vibrations1  per  second,  while  the  middle  C-string  vibrates1  272  times 
per  second.  Human  voices  from  the  deepest  bass  of  men  to  the  high- 
est treble  of  women  lie  between  80  and  1000  vibrations  per  second. 

The  upper  limit  of  hearing  varies  in  different  persons,  and  very 
curious  results  often  follow  from  this.  u  Nothing  can  be  more  sur- 
prising," says  Sir  John  Herschel,2  "  than  to  see  two  persons,  neither 
of  them  deaf,  the  one  complaining  of  the  penetrating  shrillness  of  a 
sound,  while  the  other  maintains  there  is  no  sound  at  all."  And 
Tyndall  notes  that  in  crossing  the  Alps  with  a  friend,  "the  grass  at 
each  side.of  the  path  swarmed  with  insects,  which  to  me  rent  the  air 
with  their  shrill  chirruping.  My  friend  heard  nothing  of  this,  the 
insect-music  lying  beyond  his  limit  of  audition." 

219.  Lengths  of  Sound-Waves.— If  the  temperature  of 
the  air  is  62°,  sound  travels  through  it  about  1120  feet  per 
second.     And  if  a  tuning-fork  that  vibrates  256  times  per 
second  is  sounded,  at  the  end  of  1  second  the  first  wave  of 
sound  must  be  1120  feet  from  the  fork,  and  the  256th  has 
just  left  the  fork,  and  so  scattered  through  the  1120  feet 
there  are  256  waves.     As  the  tuning-fork  gives  out  a  musi- 
cal sound,  the  waves  must  be  at  equal  distances  from  one 
another,  and,  therefore,  dividing  1120  feet  by  256  gives  us 
the  distance  between  any  two  successive  condensations,  or 
the  length  of  a  wave.     It  is  4  feet  4J  inches. 

When  the  temperature  of  the  air  is  82°,  a  man  is  speaking  in  a 
pitch  that  produces  120  vibrations  per  second :  what  is  the  length  of 
one  of  the  sound-waves?  Ans.  9£  feet. 

At  the  same  temperature  a  woman's  voice  is  producing  300  vibra- 
tions per  second :  what  is  the  length  of  one  of  the  sound-waves  that 
she  produces? 

SECTION  III.— MUSICAL  INSTRUMENTS. 

220.  The  Sonometer. — The  piece  of  apparatus  most  com- 
monly used  in  experimenting  with  musical  sounds  is  the 

1  The  vibrations  meant  here  and  elsewhere  are  from  one  side  of  the 
swing  across  to  the  other,  and  back  again,  sometimes  called  double 
vibrations. 

2  A  famous  English  astronomer  and  scientist,  born  1792,  died  1871, 
son  of  the  great  astronomer  Sir  William  Herschel. 

12 


134  NATURAL   PHILOSOPHY. 

sonometer.  It  is  a  long  wooden  box,  over  which  one  or 
more  wires  are  stretched  by  weights.  The  wire  rests  on 
wooden  bridges  at  the  ends  of  the  box,  and  between  them 
is  a  bridge  which  can  be  moved  anywhere  along  the  scale 


FIG.  125.— SONOMETER. 

of  inches  which  is  marked  off  under  the  wire.  If  the 
stretched  wire  be  pulled  aside 'with  the  thumb  and  finger, 
or  if  it  be  bowed  with  a  violin-bow,  a  clear  musical  sound 
will  be  produced  that  lasts  a  short  time. 

221.  The  Laws  of  Vibrating  Strings.  —  If  the  wire  be 
shortened,  by  moving  the  movable  bridge,  so  that  half  of  it 
vibrates,  it  is  found  to  make  twice  as  many  vibrations  per 
second  as  the  whole  wire.     If  one-third  of  it  is  vibrated, 
it  will  vibrate  three  times  as  fast  as  the  whole ;  if  one-fourth, 
four  times  as  fast,1  etc.     Hence, 

222.  The  First  Law. — The  number  of  vibrations  of  a  string 
is  inversely  proportional  to  its  length. 

Without  using  the  movable  bridge,  put  more  weights  on 
the  string  until  they  are  four  times  as  heavy  as  at  first, 
the  string  will  vibrate  twice  as  fast  as  at  first ;  with  nine 
times  as  much  weight  it  will  vibrate  three  times  as  fast,  etc. 
Hence, 

1  The  number  of  vibrations  can  be  counted  by  bringing  the  siren 
to  the  same  pitch  and  counting  its  vibrations  ;  or  any  one  even  slightly 
acquainted  with  music  can  tell  the  relative  number  of  vibrations  by 
the  pitch,  as  will  be  explained  in  the  next  section. 


SOUND.  135 


223.  The  Second  Law. — The  number  of  vibrations  of  a 
string  is  directly  proportional  to  the  square  root  of  its  tension. 

If  a  second  wire  of  the  same  material,  but  weighing  four 
times  as  much  to  the  yard,  be  stretched  beside  the  first  one, 
and  the  stretching-weights  and  the  lengths  are  the  same,  it 
will  vibrate  one-half  as  fast ;  one  nine  times  as  heavy  will 
vibrate  one-third  as  fast,  etc.  Hence, 

224.  The  Third  Law. — The  number  of  vibrations  of  a  string 
is  inversely  proportional  to  the  square  root  of  its  weight. 

The  Pitch  of  Vibrating  Strings. — As  the  pitch  of  musical 
sound  depends  solely  upon  the  number  of  vibrations  per 
second,  the  laws  of  vibration  are  also  the  laws  of  pitch. 

Experiment  61. — Vary  the  length  of  the  wire,  the  stretching- 
weight,  and  the  weight  of  the  wire  on  the  sonometer,  and  notice  the 
changes  in  pitch. 

Experiment  62. — Lift  the  lid  of  a  piano,  sound  the  highest  key, 
and  notice  that  the  shortest  wire1  is  struck.  Strike  the  lowest  key, 
the  longest  wire  is  struck  :  which  law  ?  Repeat  the  law  to  yourself. 
Notice  also  that  the  wires  struck  by  the  higher  keys  are  very  thin  and 
light,  while  those  struck  by  the  lower  keys  are  much  heavier  and 
have  extra  wire  wrapped  around  them  to  make  them  heavier  still : 
why  ?  Repeat  the  law. 

If  you  cannot  play  the  violin  yourself,  watch  some  one  tuning  and 
playing  one.  Why  are  some  of  the  strings  heavier  than  others? 
Which  have  the  highest  pitch  ?  What  is  peculiar  about  the  one  that 
has  the  lowest  pitch  ? 

What  eifect  does  it  have  upon  the  pitch  to  tighten  up  the  strings  in 
tuning  the  instrument?  Repeat  the  law. 

Why  does  the  player  touch  the  strings  in  diiferent  places  while 
playing?  Explain  this  fully  by  referring  to  the  law. 

225.  Sympathetic  Vibrations.  —  Experiment  64.— Sound  a 

tuning-fork,  and  set  the  end  of  the  handle  on  a  table  or  against  the 
panel  of  a  door.  It  sounds  very  much  louder  than  in  the  air.  The 
vibrations  of  the  fork  have  set  the  wood  to  vibrating  too,  and  it  sounds 
out  louder  than  the  fork. 

The  vibrations  of  the  wood  thus  caused  are  called  sym- 
pathetic vibrations.  They  are  very  commonly  produced, 
and  are  of  great  importance  in  music  and  sounds  generally. 

1  In  most  pianos  there  are  two  wires  for  each  key,  both,  of  course, 
of  the  same  length.  In  some  of  the  better  modern  pianos  there  are 
three  for  each  key. 


136  NATURAL   PHILOSOPHY. 

For  experimentation,  tuning-forks  are  very  frequently 
mounted  upon  sounding-boxes  (Fig.  126),  which  strengthen 
the  sound  as  the  table  did.  It  is 
not  necessary  that  the  sounding 
body  actually  touch  another  to  set 
it  to  vibrating.  It  may  be  done  by 
the  sound-waves  in  the  air. 

Experiment  64. — Kaise  the  lid  of  a 
piano,  lift  the  dampers  from  the  wires 
by  putting  your  foot  on  the  right  pedal, 
and  make  a  sound  over  the  strings  with 
the  voice.  The  sound-waves  set  in  mo- 
tion by  your  voice  cause  the  sounding 
parts  of  the  piano  to  vibrate,  and  when 
your  voice  stops  you  hear  the  piano 
sounding  in  exactly  the  same  pitch  as 
FIQ.  126.— TUNING-FORK  ON  your  voice  had. 

Experiment  65.— If  two  tuning-forks 
of  the  same  pitch,  mounted  on  sounding- 
boxes,  be  placed  side  by  side,  and  one  of  them  be  sounded,  the  other 
will  take  up  the  sound,  and  may  be  heard  after  the  first  is  silenced. 
But  if  the  pitch  of  one  of  them  be  lowered  by  sticking  a  small  lump 
of  wax  upon  one  of  its  prongs,  the  sounding  of  the  other  will  not  set 
this  one  to  vibrating. 

The  strings  of  a  violin  would  give  out  very  feeble  sounds 
if  they  were  not  reinforced  by  the  sympathetic  vibrations 
of  the  wooden  shell  below  them.  Underneath  the  strings 
of  a  piano  you  may  see  a  thin  board, — the  sounding-board. 
Without  that  the  sound  of  the  piano  would  be  insignificant. 

Experiment  66. — Touch  the  handle  of  a  vibrating  tuning-fork  to 
the  body  of  a  violin  or  to  the  sounding-board  of  a  piano,  and  notice 
how  it  sounds  out.  It  will  keep  on  sounding  after  you  have  taken 
away  and  silenced  your  fork.  Do  not  fail  to  notice  that  it  gives  out 
the  same  pitch  as  the  fork. 

Experiment  67. — Stretch  your  sonometer  wire,  or  one  like  it,  across 
an  open  door- way,  and  notice  the  comparative  feebleness  of  the  sound. 
You  see  why  you  have  a  wooden  box  under  your  wire. 

Professor  Tyndall  illustrated  this,  as  well  as  the  conduction  of 
sound  by  solids,  very  beautifully  in  his  lectures  in  London.  On  the 
second  floor  below  his  lecture-room  he  placed  a  piano.  A  pine  rod 
rested  on  the  sounding-board  of  the  piano  and  came  up  through  the 
floors  in  front  of  his  desk.  When  the  piano  was  played,  the  rod  was 
of  course  set  in  vibration,  but  too  feebly  to  be  heard.  When,  how- 


SOUND.  137 


ever,  Professor  Tyndall  laid  a  violin  on  the  end  of  the  rod,  the  vibra- 
tions of  the  rod  set  the  wood  of  the  violin  to  vibrating,  and  it  repro- 
duced the  music  of  the  piano  so  that  it  could  be  heard  all  over  the 
room.  A  guitar,  a  harp,  and  even  a  thin  flat  board,  when  put  in  the 
place  of  the  violin,  reproduced  every  note  of  the  piano. 

226.  Resonance. — This  capability  of  being  set  to  vibrating 
by  sound-waves  and  of  giving  forth  sound  of  the  same 
pitch  is  called  resonance.  Different  bodies  possess  it  in 
various  degrees  according  to  their  material  and  their  shape. 

Experiment  68. — Sound  the  tuning-fork  and  touch  the  end  of  the 
handle  against  your  slate  ;  a  window-pane  ;  a  book,  open  and  shut ;  a 
stone  or  brick  wall ;  a  lath-and-plaster  partition ;  iron  ;  stone ;  the 
blackboard-pointer  ;  your  hand,  etc.  Notice  the  differences  in  inten- 
sity, and  whether  they  are  due  to  the  material  or  the  shape  of  the  body. 

Eesonance  may  also  be  caused  by  sympathetic  vibrations 
of  a  body  of  air,  and  it  is  to  such  vibrations  that  the  term 
is  usually  applied. 

Experiment  69. — Fix  the  mouth  as  if  about  to  say  e,  and  bring  a 
sounding  tuning-fork  close  before  it.  Quickly  change  the  mouth  as 
if  to  say  o,  and  notice  that  the  sound  is  strengthened.  The  latter 
shape  gave  a  more  resonant  body  of  air,  hence  the  stronger  sound. 

Experiment  70. — (Fig.  127.)  Take  a  deep  glass  jar  and  hold  the 
sounding  tuning-fork  over  its  mouth.  The  sound  of  the  fork  will 
probably  be  only  slightly  strengthened.  Pour  water  into  the  jar 
quietly ;  the  resonance  increases  as  the  air-column  shortens,  until 
presently  it  becomes  very  strong.  "We  have  found  the  length  of  air- 
column  which  is  best  vibrated  by  the  waves  from  our  fork.  If  more 
water  be  poured  in,  the  resonance  decreases  again. 

Let  us  see  if  we  cannot  learn  why  one  particular  length  of  the  air- 
column  makes  the  resonance  greatest.  Fig.  128  represents  the  fork 
vibrating  over  the  jar.  As  the  prong  moves  from  its  position  of  rest 
down  to  5,  the  air  is  condensed  below  it,  and  the  condensation  moves 
down  to  the  bottom  of  the  jar  (or  to  the  surface  of  the  water)  and  is 
reflected  back  again.  In  order  that  the  vibrations  of  the  air  should 
fit  those  of  the  fork,  the  column  of  air  ought  to  be  long  enough  to 
allow  this  condensation  (after  reflection)  to  reach  the  prong  again 
just  as  the  prong  reaches  the  middle  of  the  vibration  ;  or  while  the 
prong  is  making  an  excursion  to  one  side  and  back  to  the  middle 
again,  which  is  half  a  vibration,  the  condensation  must  travel  twice 
the  length  of  the  air-column.  In  swinging  up  from  its  middle  posi- 
tion the  prong  produces  a  rarefaction,  which  must  also  travel  to  the 
bottom  of  the  column  and  back  again  while  the  prong  is  making  the 

12* 


138 


NATURAL   PHILOSOPHY. 


upper  half  of  its  vibration.  It  is  clear  that  if  the  vibrations  of  the 
air-column  did  not  thus  fit  those  of  the  fork,  they  would  interfere 
with  one  another  or  with  the  fork,  and  thus  be  weakened.  When  the 
vibrations  of  two  bodies  fit  together,  as  do  those  of  the  fork  and  the 
column  of  air  when  the  resonance  is  greatest,  they  are  said  to  be 
synchronous.1  Since  a  pulse  must  pass  along  the  air-column  four 
times  during  one  complete  vibration  of  the  fork,  the  tube  ought  to  be 
one-fourth  the  length  of  a  sound-wave  of  that  pitch.  If  the  depth 
of  the  air-column  which  sounds  loudest  for  a  fork  vibrating  256  times 
per  second  be  measured,  it  will  be  found  to  be  about  13  inches  deep, 


*  FIG.  127. 


and  we  have  found  in  Art.  219  that  a  fork  making  256  vibrations  per 
second  sends  out  waves  52£  inches  long,  which  very  accurately  con- 
firms our  reasoning. 

Fig.  129  represents  a  piece  of  apparatus  often  used  to  illustrate 
resonance.  It  consists  of  a  bell,  best  sounded  by  drawing  a  violin- 
bow  across  its  edge,  and  beside  it  a  tube  with  a  movable  bottom  that 
has  been  adjusted  to  the  right  depth  for  the  bell.  While  the  tube  is 

1  Pronounced  sink'ro-nus ;  derived  from  the  Greek,  and  meaning 
happening  at  the  same  time,  or  simultaneous. 


SOUND.  139 


at  some  distance  from  the  bell  the  latter  sounds  feeble,  but  when  we 
slide  the  tube  up  close  to  it  the  bell  sounds  surprisingly  strong. 
Move  the  tube  back  and  forth, 
and  notice  the  changes. 

The  murmuring  sound  heard 
in  a  hollow  shell  when  placed 
close  to  the  ear  is  due  to  reso- 
nance. Tyndall  says,  "  Chil- 
dren think  they  hear  in  it  the 
sound  of  the  sea.  The  noise 
is  really  due  to  the  reinforce- 
ment of  the  feeble  sounds  with 
which  even  the  stillest  air  is  Fia.  129. 

pervaded,  and  also  in  part  to 
the  noise  produced  by  the  pressure  of  the  shell  against  the  ear  itself." 

Questions. — When  the  air  has  a  temperature  of  62°,  what  is  the 
length  of  the  tube  that  will  resound  best  to  a  fork  vibrating  480 
times  per  second?  Ans.  7  inches.  What  to  one  vibrating  280  times 
per  second  ? 

Sound  travels  nearly  four  times  as  fast  in  hydrogen  as  in  air. 
Would  a  column  of  hydrogen  have  to  be  longer  or  shorter  than  a 
column  of  air  to  be  synchronous  with  a  certain  tuning-fork  ? 

227.  The  Two  Classes  of  Musical  Instruments. — Most  of 
the  musical  instruments  are  either  stringed  instruments  or 
wind  instruments.     The  piano   and  violin  are  the  most 
common  stringed  instruments.     The  music  of  all  of  this 
class  of  instruments  is  made  by  the  vibrations  of  strings, 
generally  reinforced  by  the  sympathetic  vibrations  of  sound- 
ing-boards.    In  wind  instruments  tubes  full  of  air  are  in 
some  way  set  to  vibrating,  and  these  bodies  of  air  give  out 
the  sounds.     Pipe-  and  cabinet-organs,  flutes,  horns  of  all 
kinds,  are  wind  instruments. 

228.  Interference  of  Sound. — We  have  learned  (Art.  159) 
that  in  water-waves,  when  the  highest  part  of  one  wave 
meets  the  lowest  part  of  another  of  the  same  size,  the 
two   waves   neutralize   each   other   and   produce   smooth 
water.     In  the  same  way,  when  the  condensed  part  of  one 
sound-wave  meets  the  rarefied  part  of  another,  silence  is 
produced. 


140 


NATURAL   PHILOSOPHY. 


\ 


Experiment  71. — Sound  a  tuning-fork,  hold  it  upright  a  short  dis- 
tance from  the  ear,  and  roll  it  slowly  around  between  the  thumb  and 
the  finger.  Its  sound  will  grow  fainter,  almost  or  entirely  die  out, 
then  grow  strong  again,  and  so  on  as  it  continues  sounding. 

Fig.  130,  which  rep- 
resents the  ends  of  the 
fork,  will  help  to  make 
the  cause  of  this  clear. 
When  the  prongs  are 
moving  outward,  there 
are  condensations  at  a 
and  b.  But,  as  the  air 
will  rush  in  from  the 
sides  to  fill  the  partial 
vacuum  caused  by  the 
prongs,  there  will  be 
rarefactions  at  c  and  d. 
Along  the  dotted  lines 
the  condensations  and 
rarefactions  meet  and 
destroy  one  another- 

These  are  the  lines  of  silence.  When  the  prongs  move  back  again, 
they  will  drive  the  air  out  at  the  sides  and  cause  condensations  at  c 
and  d,  while  at  a  and  b  there  will  be  rarefactions,  and  there  will  be 
the  same  interference  along  the  dotted  lines  as  before. 

In  the  experiment 
just  described,  the  fork 
must  be  held  close  to 
the  ear ;  but  by  rein- 
forcing the  sound  of 
the  fork  with  a  reso- 
nating -jar  it  may  be 
heard  all  over  a  room. 
If  the  vibrating  fork 
be  slowly  rotated  as  it 
is  held  over  the  jar,  the 
alternations  of  loud 
sounds  and  silence  will 
be  very  striking.  If  the 
fork  be  held  in  the  po- 


Fio.  130. — INTERFERENCE  OF  SOUND,  SHOWN  WITH 

A   TUNING-FORK. 


Fio.  131. 


sition  of  silence,  and  a 
pasteboard  tube  be  slipped  over  one  prong,  as  shown  in  Fig.  131,  the 


SOUND. 


141 


sound  will  swell  out  as  loud  as  ever.  The  vibrations  of  the  un- 
covered prong  are  protected  from  the  vibrations  of  the  other,  and  are 
no  longer  quenched. 

229.  How  the  Vibrations  of  the  Air-Columns  are  excited 
in  Wind-instruments. — Fig.  132  shows  a  complete  and  a 
sectional  view  of  an  organ-pipe  from 
a  pipe-organ  or  large  church-organ. 
The  air  is  forced  up  from  below  by 
a  bellows,  and,  rushing  against  the 
sharp  edge  of  an  opening  in  the  pipe, 
is  thrown  into  vibrations,  which  com- 
municate themselves  to  the  column 
of  air  in  the  pipe.  It  is  much  like 
an  ordinary  willow  whistle.  In  a 
cabinet-organ  the  air  is  set  in  motion 
by  the  vibration  of  reeds.  A  reed  is 
a  strip  of  brass,  fastened  only  at  one 
end,  and  arranged  so  as  to  vibrate 
in  an  opening  which  it  almost  fills. 
There  is  a  reed  of  a  different  pitch 
for  every  key,  and  pressing  down 
that  key  opens  the  way  for  the  air 
to  pass  from  the  bellows  to  its  reed. 
The  reed  is  made  to  vibrate  by 
forcing  air  from  a  bellows  through 
the  opening  around  the  reed.  The 
vibration  of  the  reed  sets  the  air 
about  it  in  motion.  The  melodeon. 
which  has  been  almost  superseded 
by  the  cabinet-organ,  also  produces  its  music  by  reeds  of 
this  kind,  and  in  a  very  similar  way.  (Fig.  133.)  The 
accordion  is  almost  literally  a  hand  cabinet-organ,  with 
bellows  and  reeds.  The  common  mouth-organ  is  a  reed 
instrument,  and  its  reeds  can  easily  be  seen. 

Experiment  72. — Take  a  piece  of  wheat-  or  rye-straw,  and  slit  a 
tongue  in  it  down  to  a  joint,  as  shown  in  Fig.  134.  This  tongue  is  a 
reed,  and  the  whole  is  a  simple  reed  instrument.  Blow  into  the  open 


FIG.  132.— ORGAN-PIPES. 


142 


NATURAL   PHILOSOPHY. 


end,  and  note  the  pitch.     Cut  an  inch  or  two  off  the  open  end  and 
blow  again  ;  the  pitch  is  higher.     Cut  off  another  piece  ;  the  pitch  is 


FIG.  133.— CABINET-ORGAN  KEEDS. 


still  higher.  Careful  experiments  show  that,  so  far  as  length  is  con- 
cerned, the  law  of  the  sound-vibrations  of  a  column  of  air  is  the  same 
as  those  of  a  string :  the  number  of  vibrations  of  a  column  of  air  is 
inversely  proportional  to  its  length. 


FIG.  134.— REED  MADE  or  WHEAT-STRAW. 

The  clarionet  has  a  wooden  reed  in  the  mouth-piece. 

The  flute  and  the  fife  are  played  by  blowing  against  the 
sharp  edge  of  an  opening  in  the  side 
of  the  tube.  The  vibrations  are 
caused  very  much  in  the  same  way 
as  in  the  pipe-organ,  and  in  the  same 
way  as  when  one  whistles  in  a  key. 
In  a  cornet  or  a  horn  the  lips 
of  the  player,  pressed  against  the 
mouth-piece,  act  as  reeds. 

230.  The  Human  Voice,— The 
voice  is  produced  in  the  upper  part 
of  the  windpipe:  the  "Adam's 

FIG.  135.-THE  VOCAL  CORDS,   apple"  marks  the  place.      Fig.  135 

shows  the  vocal  apparatus  as  looked 

down  upon  by  means  of  a  laryngoscope.1   o  is  a  slit  through 


1  Pronounced  la-ring'go-skop.    A  pair  of  mirrors  so  arranged  as  to 
show  this  part  of  the  throat. 


SOUND.  143 


which  the  air  passes  to  and  from  the  lungs.  On  either  side 
of  this  is  a  membrane,  v,  v,  projecting  from  the  sides  of  the 
windpipe.  These  membranes  are  called  the  vocal  cords,  al- 
though they  are  not  cords  at  all.  In  ordinary  breathing 
these  cords  are  loose  and  close  to  the  sides  of  the  windpipe, 
leaving  a  wide  opening  between  them.  But  when  we  wish 
to  make  sounds,  they  are,  by  muscular  action,  stretched 
tight  and  brought  close  together,  so  as  to  leave  only  a 
narrow  slit  between  them.  The  air  from  the  lungs  passing 
between  them  sets  them  in  vibration,  and  their  vibrations 
produce  the  sounds  of  the  voice,  just  as  the  reeds  of  a 
cabinet-organ  produce  sound.  The  human  voice  is  a  reed 
wind-instrument. 

The  vocal  cords  can  only  make  sounds  of  different  pitch 
and  loudness.  The  resonance  of  the  cavity  of  the  mouth 
and  nose,  varying  with  its  shape, "changes  the  sounds  of  the 
vocal  cords  into  the  distinct  vowels  and  consonants.  The 
pitch  of  one's  voice  depends  upon  the  length  and  thickness 
of  the  vocal  cords.  The  ordinary  tones  of  women's  voices 
produce  more  than  twice  as  many  vibrations  per  second  as 
those  of  men's  voices  (Art.  218). 

Experiment  73. — Notice  that  women  or  girls,  and  boys  whose  voices 
have  not  changed,  show  no  Adam's  apple  in  the  neck,  but  that  it  is 
prominent  in  men ,  and  especially  in  men  with  bass  voices :  why  is  this  ? 

Experiment  74. — Get  from  a  butcher  the  upper  part  of  the  wind- 
pipe of  a  hog  or  other  slaughtered  animal,  cut  it  open  from  front  to 
back,  and  examine  the  vocal  cords.  They  are  very  much  like  yours. 
You  will  see  what  will  look  like  two  pairs  of  cords.  The  lower  ones 
are  the  true  vocal  cords ;  the  upper  ones  perhaps  serve  to  modify  the 
sounds  which  the  lower  ones  alone  produce. 

231.  Vibrations  of  Strings  in  Parts.— Experiment  75.— Touch 

the  middle  of  the  sonometer  wire  with  your  finger,  or  with  a  feather, 
and  draw  the  bow  across  the  middle  of  one  half.  The  middle  point 
which  was  held  by  the  feather  is  stationary,  but  each  half  of  the 
wire  is  vibrating.  Set  a  rider,  made  by  folding  a  bit  of  paper  into 
the  shape  of  a  V,  upon  the  middle  of  either  half,  it  is  thrown  off. 
Set  it  upon  the  middle  of  the  wire,  it  stays  there  :  why  ? 

Experiment  76. — Again,  touch  the  wire  at  one-third  the  distance 
from  one  end,  and  draw  the  bow  across  the  middle  of  one  third.  The 
wire  will  vibrate  in  thirds.  Test  the  points  of  greatest  vibration  and 
of  no  vibration  with  the  riders.  In  the  same  way  the  wire  may  be 
made  to  vibrate  in  fourths,  fifths,  etc. 


144 


NATURAL   PHILOSOPHY. 


The  parts  of  the  wire  which  we  have  made  to  vibrate 
are  called  segments.  The  points  between  the  segments, 
where  there  was  no  motion,  are  the  nodes.  When  a  string 
is  thus  vibrating  in  parts  only,  its  pitch  is  higher  than  if 


Fio.  136.— STRING  VIBRATING  IN  HALVES. 


it  were  vibrating  as  a  whole,  for,  according  to  the  first  law 
of  vibrating  strings,  when  it  vibrates  in  halves  each  seg- 
ment vibrates  twice  as  fast  as  the  whole  string  would ;  when 
in  thirds,  each  segment  vibrates  three  times  as  fast,  etc. 
When  a  string  vibrates  in  parts,  the  segments  are  always 


FIG.  137. — STRING  VIBRATING  IN  THIRDS. 


equal;  each  is  an  exact  division  of  the  whole  string.  And 
again,  when  a  string  vibrates  in  parts,  any  two  consecutive 
parts  are  always  moving  in  opposite  directions.  Thus,  in  Fig. 
136;  while  one  half  moves  up  the  other  half  is  coming  down ; 


SOUND.  145 


and  in  Fig.  137  the  two  end  segments  are  swinging  in  one 
direction  while  the  middle  one  swings  in  the  other. 

232.  A  String  may  vibrate  in  Parts  and  as  a  Whole  at 
the  Same  Time, — If  the  wire  of  the  sonometer  be  plucked 
near  one  end,  it  will  vibrate  in  parts  and  as  a  whole  at  the 
same  time.  Fig.  138  shows  a  string  thus  vibrating  as  a 


FIG.  138. — STRING  VIBRATING  AS  A  WHOLE  AND  IN  HALVES. 

whole  and  in  halves.  The  middle  arrows  show  the  direc- 
tion of  the  whole  string,  the  others  show  the  smaller  and 
quicker  vibrations  of  the  halves.  In  the  same  way  it  may, 
while  vibrating  as  a  whole,  be  also  vibrating  in  thirds, 
fourths,  etc.  And  it  may  even  be  vibrating  as  a  whole,  in 
halves,  thirds,  fourths,  etc.,  all  at  the  same  time. 

233.  Vibrations  of  Air-Columns  in  Parts. — The  air  in  an 
organ  or  other  pipe  may  vibrate  as  a  whole  or  in  parts,  or 
as  a  whole  and  in  parts  at  the  same  time,  just  as  a  string 
may. 

Experiment  77. — Take  a  tube  of  glass  or  other  material,  about  18 
inches  long  and  from  a  quarter  to  half  an  inch  in  diameter,  close  one 
end  with  the  finger,  and  blow  rather  gently  across  the  other,  and  you 
hear  a  low  note,  the  lowest  or  the  fundamental  note  of  your  tube :  the 
air-column  is  vibrating  as  a  whole.  Blow  again  and  strongly,  and 
you  make  a  much  higher  note.  The  air-column  is  vibrating  in  seg- 
ments. Try  the  same  experiments  with  the  lower  end  of  the  tube 
open  :  the  results  are  like  the  others. 

In  trying  the  above  experiment  you  must  have  noticed  that  the 

lowest  note  of  the  open  pipe  was  much  higher  than  the  lowest  note 

of  the  closed  pipe.     This  is  because  the  air  in  a  pipe  open  at  both 

ends  can  never  vibrate  as  a  whole  :  there  is  no  bottom  to  the  pipe  to 

a         k  13 


146  NATURAL   PHILOSOPHY. 


send  the  wave  back  again.  The  lowest  note  that  such  a  pipe  can 
give  is  when  it  is- vibrating  in  halves  ;  then  the  two  waves  meet  each 
other  at  the  middle  and  turn  each  other  back.  Just  at  the  middle 
there  is  no  motion  of  the  particles  :  there  is  a  node  there.  A  pipe 
open  at  both  ends  gives  the  same  pitch  as  one  of  half  its  length  which 
is  closed  at  one  end.  In  fact,  it  is  just  the  same  as  two  closed  pipes 
with  the  closed  ends  together.  The  keys  in  horns  and  the  finger-holes 
in  flutes,  etc.,  enable  the  player  to  change  the  nodes  and  the  lengths 
of  the  vibrating  columns  of  air,  and  therefore  to  vary  the  pitch  of 
his  tones. 

234.  Overtones. — When  a  whole  string,  or  a  column  of  air, 
and  its  various  parts  are  vibrating  together,  the  vibrating 
parts  also  produce  tones,  higher  in  pitch,  of  course,  than 
that  of  the  whole  string.  These  are  called  overtones.  The 
overtones  cannot  usually  be  distinguished  from  the  funda- 
mental tone  by  ordinary  ears,  and  so  they  do  not  affect  the 
pitch  of  the  sound,  which  is  that  of  the  string  as  a  whole ; 
but  they  do  change  the  character  of  the  tone,  as  we  shall 
see  hereafter. 

Helmholtz1  has  invented  an  instrument  to  enable  us  to  detect  the 
overtones  in  a  compound  sound.  It  is  called  a  resonator,  and  is 

shown  in  Fig.  139.  This  is 
made  of  just  the  size  to  be 
resonant  to  the  sound  made 
by  halves  of  a  certain  string. 
When  the  string  is  sounding 
as  a  whole,  and  also  in  halves, 
the  small  end  of  the  resonator 
is  put  into  the  ear,  and  by  its 
resonance  it  so  strengthens  the 
sound  of  the  halves  that  they 
can  be  distinctly  heard.  An- 
other resonator  of  different 
FIG.  139.— HELMHOLTZ'S  EESONATOE.  size  will  strengthen  the  sound 

of   the  thirds   enough    to  be 

heard,  another  the  fourths,  and  so  on.  By  having  a  whole  set  of 
these  resonators,  all  the  overtones  in  a  compound  sound  can  be  dis- 

1  H.  L.  F.  Helmholtz,  1821-,  Professor  of  Physics  in  the  University 
of  Berlin,  and  one  of  the  greatest  scientists  of  this  or  any  other  age. 


SOUND. 


147 


Fio.  140. 


tinguished.  These  instruments  show  that  the  sounds  of  almost  all 
our  musical  instruments  are  very  complex.  The  strings  of  pianos 
and  violins,  the  reeds  of  organs,  etc.,  besides  sounding  as  wholes,  are 
also  vibrating  in  halves,  thirds,  fourths,  fifths,  and  often  many  more 
parts.  The  human  voice  has  many  overtones. 

235.  Manometric  Flames.  —  Koenig,  an  instrument-maker  of 
Paris,  has  devised  an  apparatus 
which  shows  the  effects  of  the  over- 
tones very  beautifully.  It  consists 
of  two  parts,  one  of  which  is  shown 
in  Fig.  140.  m  is  the  mouth-piece  of 
a  tube,  across  the  other  end  of  which 
is  stretched  a  piece  of  india-rubber, 

r,  f  is  a  gas-burner,  fed  by  the  tube  g.  The  gas-tube  is  separated  from 
the  other  only  by  the  thin  sheet  of  rubber.  The 
vibrations  of  the  voice  sounding  at  tn  set  the  rub- 
ber partition  to  vibrating,  and  drive  out  the  gas 
in  puffs.  These  cause  changes  in  the  height  of 
the  flame,  but  they  are  too  rapid  to  be  noticed, 
and  the  gas-flame  looks  to  the  eye  to  be  steady. 
But  when  a  square  box  having  its  four  sides 
covered  with  mirrors  (Fig.  141)  is  rapidly  ro- 
tated in  front  of  the  flame,  its  changes  can  be 
seen. 

Fig.  142  shows  the  various  forms  that  may  be 
produced.  1  shows  the  reflection  of  the  gas- 
flame  when  the  mirror  is  stationary.  2  is  the 
reflection  when  the  mirror  revolves  without  any 
sound  being  made  in  the  tube.  3  is  a  low,  simple  sound,  with  no  over- 
tones. 4  is  a  higher  simple  sound,  but  with  no  overtones.  In  5  the 
first  overtone  (in  halves)  is  sounding  with  the  fundamental,  only 
every  other  vibration  of  the  overtone  being  seen,  the  others  are  united 
with  the  fundamental.  In  6  the  second  overtones  (in  thirds)  are 
vibrating  with  the  fundamental.1 

Almost  any  sound  can  be  analyzed  with  this  instrument,  making 
very  interesting  and  curious  experiments. 

236.  Character  of  Sound.  —  Besides  pitch  and  loudness, 

1  3  and  4  can  be  produced  by  singing  into  the  tube  oo  as  in  pool  ;  5, 
by  singing  a  in  B[j  (second  space  below  the  treble  clef)  ;  6,  by  singing 
a  in  the  note  F.  (From  Mayer's  Sound,  p.  160.) 


FJQ  141< 


148 


NATURAL   PHILOSOPHY. 


sound  has  another  quality.  A  piano,  a  violin,  and  a  human 
voice  may  all  sound  with  the  same  pitch  and  the  same 
loudness,  and  yet  they  sound  very  unlike ;  any  one  can  tell 
them  apart.  This  quality  which  distinguishes  different 


'3  '          ' 


4- 


FIG.  142. — VIBRATIONS  SHOWN  BY  MANOMETRIC  FLAME  APPARATUS. 

kinds  of  sounds  from  one  another  is  called  character,  or 
timbre.  The  character  of  sounds  has  been  found  to  be  wholly 
due  to  the  overtones.  If  a  sounding  body  is  vibrating  only 
as  a  whole,  and  not  in  parts,  or  if  while  vibrating  as  a 


SOUND.  149 


whole  only  the  halves,  and  perhaps  the  thirds,  are  also 
vibrating,  its  sound  is  pure  or  simple.  This  is  the  case 
with  a  tuning-fork  or  an  organ-pipe.  But  if  a  sounding 
body  while  vibrating  as  a  whole  is  also  vibrating  in  many 
different  divisions  at  the  same  time,  its  sound,  though  of 
the  same  pitch  as  the  other,  has  a  very  different  character : 
it  is  more  "  brilliant."  The  sounds  of  the  violin,  horn,  and 
cymbals  are  good  examples. 

237.  The  Three  dualities  of  Sound. — The  pitch  of  sound 
depends  wholly  upon  the  rapidity  of  the  vibrations.     The 
loudness  of  sound  depends  wholly  upon  the  amplitude,  or 
length  of  swing,  of  the  vibrations.     The  character  of  sound 
depends  upon  the  number  of  overtones,  or  vibrations  of 
parts,  that  are  mingled  with  the  fundamental  sound.     All 
the  difference  between  musical  sounds  of  any  kind  is  made 
by  one  or  more  of  these  three  qualities. 

238.  Vibration  of  Plates  in  Parts.— Experiment   78.— Get  a 
piece  of  good  window-glass  about  six  inches  square,  rub  its  sharp 
edges  smooth  with  a  grindstone.     Clamp  it 

in  the  middle  with  a  vise  like  that  shown 

in  Fig.  143,  which  has  been  fastened  to  the 

edge  of  a  table  by  the  lower  screw.    Scatter 

writing-sand  over  the  glass,  and  draw  a 

well-resined   heavy   bow  across   the   edge 

near  one  corner,  while  touching  the  middle 

of  another  edge  with  the  finger.     The  sand  FIG.  143. 

will  arrange  itself  in  lines  as  in  Fig.  144. 

Again,  touch  the  glass  at  one  corner,  and  draw  the  bow  across  the 

middle  of  one  edge,  Fig.  145  will  be  produced. 

These  are  called  Chladni's l  Figures.  The  finger  holds  the 
glass  still  where  it  touches  it,  and  starts  a  node  there.  The 
glass  vibrates  in  parts,  and  shakes  the  sand  gradually  to  the 
nodal  lines  between  the  vibrating  parts  where  there  is  no 
vibration.  As  with  strings  and  columns  of  air,  any  two 
consecutive  segments  are  always  vibrating  in  opposite  di- 
rections. Fig.  146  shows  some  of  the  many  sand-figures 

1  E.  F.  F.  Chladni  (klad'ne),  1756-1827,— a  German  natural  phi- 
losopher. 

13* 


150 


NATURAL   PHILOSOPHY. 


that  have  been  thus  produced  by  touching  and  bowing  the 
plate  in  different  ways. 

Bells,  gongs,  cymbals,  etc.,  vibrate  in  parts  as  these  plates 


FIG.  144. 


FIG.  145. 


do,  and  both  their  fundamental  tones  and  their  overtones 
are  due  to  such  vibrations. 

SECTION  IV.-MUSIC. 

239.  The  Scale. — There  is  a  regular  succession  of  eight 
sounds  of  increasing  pitch  used  by  all  persons  in  singing 
or  playing  any  musical  instrument,  called  the  scale.     The 
names  of  these  sounds  as  they  are  used  in  singing  are  do, 
re,  mi,  fa,  sol,  la,  si,  do.1     In  instrumental  music  the  sounds 
of  the  scale  are  denoted  by  the  following  letters :  C,  D,  B, 
F,  G,  A,  B,  C.     The  first  or  lower  do,  or  C,  is  called  the  key- 
note, or  fundamental  note,  of  the  scale. 

Almost  all  who  study  this  book  are  familiar  with  the  scale,  and 
can  sing  it  for  themselves.  If  any  cannot,  they  may  hear  it  by 
striking  eight  successive  white  keys  of  a  piano  or  organ,  beginning 
with  C. 

240.  The  Derivation  of  the  Scale, — To  derive  the  scale,  let 
us  use  our  sonometer  again.     It  will  be  convenient  to  have 
the  wire  30  inches  long  to  start  with.     If  it  is  longer  than 
that,  we  may  use  that  much  of  it  by  putting  a  bridge  under 
it,  30  inches  from  one  end. 

To  produce  do,  sound  the  whole  string. 


1  Pronounced  do,  ra,  me,  fah,  sol,  lah,  se,  do. 


SOUND. 


151 


Fio.  146.— SAND-FIGURES. 


152  NATURAL   PHILOSOPHY. 


To  produce  re,  move  the  bridge  so  as  to  make  the  wire 
|  as  long  as  at  first  (26f  inches),  and  sound  it. 

To  produce  mi,  move  the  bridge  so  as  to  make  the  wire 
|  as  long  as  at  first  (24  inches),  and  sound  it. 

To  produce  fa,  move  the  bridge  so  as  to  make  the  wire 
|  as  long  as  at  first  (22J  inches),  and  sound  it. 

To  produce  sol,  move  the  bridge  so  as  to  make  the  wire 
f  as  long  as  at  first  (20  inches),  and  sound  it. 

To  produce  la,  move  the  bridge  so  as  to  make  the  wire 
f  as  long  as  at  first  (18  inches),  and  sound  it. 

To  produce  si,  move  the  bridge  so  as  to  make  the  wire 
-^  as  long  as  at  first  (16  inches),  and  sound  it. 

To  produce  upper  do,  move  the  bridge  so  as  to  make  the 
wire  ^  as  long  as  at  first  (15  inches),  and  sound  it. 

1>  f  >  f  >  t>  f>  f  >  -fsi  i>  are  tne  proportionate  lengths  which 
a  string  (whose  tension  is  unchanged)  must  invariably 
have  to  produce  the  common  scale.  The  eight  sounds  are 
called  an  octave.1 

241.  The  Number  of  Vibrations  of  the  Notes  of  the  Scale. 
— According  to  the  first  law  of  vibrating  strings,  the  num- 
ber of  vibrations  of  a  string  is  inversely  proportional  to  its 
length.  Therefore,  if  we  invert  the  fractions  given  above, 
we  have  the  relative  numbers  of  vibrations  per  second 
which  are  produced  when  the  successive  notes  of  the  scale 
are  sounded.  They  are  as  follows :  1,  f ,  f,  f ,  f ,  f,  l-/,  2. 
It  will  be  noticed  that  the  upper  do,  or  C,  is  produced  by 
exactly  twice  as  many  vibrations  as  the  lower  one.  This 
note  is  called  the  octave  of  the  one  below,  and  this  use  of 
the  word  octave  is  rather  more  common  than  the  use  given 
in  the  preceding  paragraph.  When  the  octave  of  a  note  is 
sounded  with  the  voice  or  with  any  instrument,  twice  as 
many  vibrations  are  invariably  produced. 

If  lower  do  is  produced  by  24  vibrations  per  second,  how  many 
vibrations  will  produce  the  succeeding  notes  of  the  scale  ? 

1  From  the  Latin  octavus,  meaning  eighth. 


SOUND.  153 


242.  The  Repetition  of  the  Scale. — In  any  scale  the  upper 
do  is  the  lower  do,  or  key-note,  of  the  next  octave.     The 
sounds  of  this  octave  are  denoted  by  the  same  names  or 
letters  as  those  of  the  octave  below.     The  notes  of  this  oc- 
tave are  produced  by  strings  having  the  same  proportion 
to  the  length  of  the  string  sounding  its  key-note  as  the 
notes  of  the  octave  below  had  to  theirs.     And  the  ratios 
of  the  numbers  of  vibrations  are  just  the  same  as  before.   In 
the  same  way  the  scale  is  repeated  in  every  seven  notes 
above  or  below  the  one  we  have  started  with  to  the  upper 
and  lower  limits  of  audibility  (Art.  218).     Every  note,  no 
matter  how  made,  is  produced  by  twice  as  many  vibrations 
as  the  note  of  the  same   name  in  the  octave  below,  four 
times  as  many  as  the  one  in  the  second  octave  below,  etc. 

Questions. — The  upper  do  produced  according  to  the  directions 
given  in  Art.  240  was  made  by  the  vibrations  of  a  wire  15  inches  long  : 
what  must  be  the  successive  lengths  of  the  wire  to  produce  the  notes 
of  the  octave  above,  of  the  second  octave  above,  of  the  octave  below? 

If  the  key-note  of  a  scale  is  produced  by  24  vibrations  per  second, 
how  many  vibrations  will  be  necessary  to  produce  the  notes  of  the 
octave  above  ?  of  the  second  octave  above  ?  How  many  of  the  notes 
of  the  octave  below  can  be  produced  ?  Why  can  they  not  all  be  pro- 
duced ? 

243.  The  Fixing  of  the  Pitch  of  the  Key-Note.  —  Any 

pitch  whatever  may  be  taken  for  the  key-note,  and  the 
different  notes  will  range  above  or  below  this,  according 
to  the  laws  just  given. 

One  person  may  sing  a  piece  of  music  using  a  key-note  of  a  certain 
pitch.  A  second  person  may  take  for  his  key-note  the  pitch  which 
the  first  gave  to  re  and  sing  the  same  piece  through.  Each  of  his 
sounds  will  of  course  be  one  note  higher  than  those  of  the  other  singer. 
A  third  singer  may  take  the  pitch  of  the  sol  of  the  first  for  his  key- 
note ;  and  so  on.  This  is  very  noticeable  when  different  persons  start 
tunes  without  the  aid  of  instruments.  The  natural  limits  of  the 
human  voice,  however,  confine  us  in  our  choice  of  the  pitch  of  the 
key-note  to  rather  narrow  limits,  varying  according  to  the  compass 
of  the  singer's  voice  and  the  range  of  the  piece  of  music  sung. 
Leaders  of  vocal  music  often  use  tuning-forks  in  order  to  get  the 
most  suitable  pitch. 

Piano-tuners  use  tuning-forks  or  whistles,  which  always  make  a 


154  NATURAL   PHILOSOPHY. 

certain  known  number  of  vibrations  per  second,  and  tune  pianos  by 
them.  In  the  best  American  pianos  middle  0  makes  268  vibrations 
per  second. 

244.  Intervals  between  the  Notes  of  the  Scale  vary.— 

The  following  numbers  are  the  answers  to  the  problem 
given  in  Art.  241,  and  are  the  relative  numbers  of  the 

do       re      mi      fa     sol 

vibrations  of  the  notes  of  any  scale, — viz.:  24,  27,  30,  32,  36, 

la      si      do 

40,  45,  48.  Ee  is  produced  by  •£%  or  -|  more  vibrations  than 
do,  mi  by  -1-  more  than  re,  fa  by  j1^  more  than  mi ;  from  fa 
to  sol  and  from  la  to  si  the  increase  is  again  -J-,  from  sol  to 
la  1,  and  from  si  to  do  y1-  again.  Thus  we  see  that  in  three 
of  the  intervals  there  is  an  increase  of  -J.  in  the  number  of 
vibrations,  in  two  of  the  others  an  increase  of  £,  and  in  the 
remaining  two  an  increase  of  only  -fa.  The  five  longer 
intervals  are  called  whole  tones,  although  they  are  not  all 
of  the  same  length,  as  we  have  seen.  The  two  shorter 
ones  are  called  half  tones,  although  they  are  really  longer 
than  half  of  any  of  the  whole  tones,  as  you  may  see  by 
comparing  -Jg.  with  the  halves  of  -J-  and  -J-.  In  every  common 
scale  the  intervals  between  the  notes  are  in  exactly  these 
proportions,  and  their  order  never  varies. 

A  scale  is  sometimes  used  which  is  made  by  inserting  an  extra  note 
in  the  middle  of  each  whole  tone:  this  gives  us  thirteen  notes  in  the 
scale,  all  about  the  same  distance  apart.  This  is  called  the  chromatic l 
scale.  But  it  is  not  natural  to  sing  the  scale  with  half  tones  any- 
where else  than  between  the  third  and  fourth  and  the  seventh  and 
eighth  notes,  so  that  few  people  can  sing  the  chromatic  scale.  When 
any  other  than  the  natural  half  tones  are  wanted  in  a  piece  of  music, 
the  composer  usually  transposes  the  scale;  that  is,  he  starts  with  his 
key-note  a  little  higher  or  lower  than  the  do  of  the  ordinary  or 
natural  scale,  and  thus  brings  the  regular  half  tones  just  where  he 
wants  a  half  interval  between  two  of  his  notes  to  come. 

245.  Temperament, — If  a  piano  or  an  organ  is  tuned  according 
to  the  natural  scale,  from  C  to  D  there  is  an  increase  of  J  in  the  number 


1  From  the  Greek  word  meaning  color,  because  these  inserted  tones 
used  to  be  represented  in  colors. 


SOUND.  155 


of  vibrations,  from  D  to  E  of  £,  from  E  to  F  of  ^,  etc.  If,  then, 
one  should  play  upon  such  an  instrument  a  piece  of  music  in  which 
the  key-note  is  D,  the  interval  between  that  and  the  next  key  would 
be  only  ^  instead  of  £,  so  that  it  would  not  give  correctly  the  second 
note  of  the  scale.  The  next  key,  T^  higher,  would  not  be  a  correct 
half  note  between  the  second  and  third  notes  of  our  scale,  as  it  should 
be,  and  so  on  through  the  scale.  Not  one  interval  in  our  scale  would 
be  correct.  The  same  would  be  true  of  every  other  scale ;  none  but 
the  one  in  which  the  instrument  was  tuned  could  be  played  upon  it 
correctly.  This  is  partly  corrected  by  the  tuner  distributing  these 
errors  equally  over  all  the  scales.  This  distribution  of  these  errors  is 
called  temperament.  The  result  is  that  no  scale  on  a  piano  or  an 
organ  is  absolutely  correct,  but  the  errors  in  any  are  so  slight  that 
most  persons  cannot  notice  them.  If  the  instrument  were  tuned  cor- 
rectly for  any  one  scale  it  would  sound  very  badly  when  played  in  any 
of  the  others.  The  piano  and  the  organ,  therefore,  are  not  perfect 
instruments,  and  can  never  make  perfect  music.  But  in  the  violin 
and  the  flute  the  pitch  is  controlled  by  the  player,  and  they  may  in 
the  hands  of  a  skilful  player  produce  perfect  music. 

246.  Beats. — Experiment  79. — On  a  piano,  or,  better  still,  on  a 
cabinet-organ,  sound  together  the  lowest  key  and  the  black  key  next 
to  it.  Mingled  with  the  sounds  of  the  two  keys  you  will  notice  a 
peculiar  quivering  sound.  These  quivers,  or  bursts,  of  sound,  which 
on  the  organ  or  piano  are  entirely  too  rapid  to  be  counted,  are  called 
beats. 

To  understand  the  cause  of  these  beats,  we  must  go  back 
to  the  interference  of  sound-waves,  about  which  we  learned 
in  Art.  228.  Let  us  suppose  that  two  sound-waves,  one 
vibrating  100  times  per  second  and  the  other  101  times  per 
second,  start  out  together.  At  the  start  their  condensa- 
tions will  coincide;  they  will  strengthen  each  other  and 
make  a  louder  sound  than  either  would  alone.  After  half 
a  second  one  is  at  the  end  of  exactly  fifty  vibrations,  and 
is,  we  may  suppose,  at  its  greatest  condensation,  but  the 
other  is  at  the  end  of  fifty  and  a  half  vibrations,  so  that  it 
must  be  at  its  greatest  rarefaction.  There  the  two  sounds 
would  destroy  each  other.  At  the  end  of  the  second  the 
100th  condensation  of  one  coincides  with  the  101st  con- 
densation of  the  other,  and  they  strengthen  each  other 


156  NATURAL  PHILOSOPHY. 

again.  These  will  be  repeated  as  long  as  the  sounds  can 
be  heard.  These  alternate  strengthenings  and  quenchings 
of  the  sound  cause  the  beats. 

It  is  clear  that  in  the  illustration  just  taken  there  would  be  one  beat 
each  second  ;  and  the  same  would  be  true  with  any  two  sounds,  one 
of  which  vibrates  once  oftener  than  the  other  in  a  second.  If  one 
has  100  and  the  other  102  vibrations  per  second,  at  the  middle  one 
wave  is  at  the  50th  and  the  other  at  the  51st  condensation.  These 
strengthen  each  other  twice  in  each  second.  Again,  if  one  vibrated 
100  and  another  105  times  per  second,  the  20th  condensation  of  one 
would  strengthen  the  21st  of  the  other ;  the  40th  of  the  one,  the  42d 
of  the  other ;  the  condensations  coincide  five  times,  or  there  are  five 
beats,  each  second.  The  number  of  beats  in  a  second  is  equal  to  the 
difference  in  the  number  of  vibrations  which  the  two  sounds  make 
per  second. 

Beats  can  be  made  much  better  than  on  a  piano  or  an  organ  by 
using  two  large  tuning-forks  of  the  same  pitch,  mounted  on  sound- 
ing-boxes, and  loading  one  of  them  with  a  little  wax.  By  increasing 
the  wax  the  beats  are  made  more  frequent. 

Beats  are  always  produced  when  two  notes  of  different 
pitch  are  sounded  together.  Generally  they  cannot  be 
noticed,  but  nevertheless  they  have  a  most  important  effect 
upon  the  sound,  as  we  shall  see  in  the  next  paragraph. 

247.  Harmony  and  Discord. — "  If,  towards  sunset,  you 
walk  on  the  shady  side  of  a  picket-fence,  flashes  of  light 
will  enter  your  eye  every  time  you  come  to  an  opening 
between  the  pales.  These  flashes,  coming  slowly  one  after 
the  other,  cause  a  very  disagreeable  sensation  in  the  eye. 
Similarly,  if  flashes  or  pulses  of  sound  enter  the  ear,  they 
cause  a  disagreeable  sensation."1  When  two  notes  of 
different  pitch  are  sounded  together,  beats  are  always  pro- 
duced. If  these  are  very  slow,  the  effect  is  not  particularly 
disagreeable,  but  if  they  are  numerous,  as  when  any  two 
contiguous  keys  of  a  piano  or  an  organ  are  sounded,  they 
produce  a  harsh  sound,  which  we  all  recognize  as  a  discord. 

"  But  if  the  flashes  of  light  or  beats  of  sound  succeed 

1  Mayer's  Sound,  pp.  174,  175. 


SOUND.  157 


one  another  so  rapidly  that  the  sensation  of  one  flash  or 
beat  remains  till  the  next  arrives,  you  will  have  continuous 
sensations  that  are  not  unpleasant.  In  other  words,  con- 
tinuous sensations  are  pleasant,  but  discontinuous  or  broken 
sensations  are  disagreeable."1  If,  therefore,  the  beats  are 
very  numerous,  we  have  harmony. 

For  instance,  when  a  note  and  its  octave  are  sounded  together,  every 
other  vibration  of  the  upper  note  and  every  vibration  of  the  lower 
coincide :  we  have  the  greatest  possible  number  of  coincidences  or 
beats  that  two  sounds  of  different  pitch  can  have,  and  we  have  what 
is  universally  recognized  as  the  most  perfect  harmony.  When  men 
and  women  sing  together  the  same  part  of  a  piece  of  music,  the 
women's  voices  are  just  an  octave  above  the  men's.  Again,  when  do 
and  sol  are  sounded  together,  every  third  vibration  of  sol  coincides 
with  every  second  vibration  of  do ;  the  next  most  numerous  coinci- 
dences that  are  possible  produce  what  is  well  known  to  be  the  next 
best  harmony.  For  the  same  reason  the  first  and  fourth  notes,  and 
the  first  and  third,  make  pleasing  sounds.  But  do  and  re  only  coin- 
cide at  every  eighth  vibration  of  do,  and  si  and  do  at  every  fifteenth 
of  si.  Here  the  beats  are  not  rapid  enough  to  be  pleasant,  and  these 
make  discords. 

Why  very  many  beats  are  agreeable  and  produce  harmony,  while 
a  less  number  are  disagreeable  and  produce  discord,  may  be  illustrated 
by  remembering  that  a  single  cobweb,  or  even  a  considerable  number 
of  cobwebs,  if  brushed  across  one's  face,  tickle  it  very  disagreeably ; 
yet  if  these  cobwebs  could  be  woven  into  a  piece  of  velvet,  it  would 
produce  the  same  pleasant  sensation  that  a  piece  of  ordinary  velvet 
does  when  rubbed  over  one's  face. 

248.  Harmonics. — We  have  learned  (Art.  232)  that  when  a  string, 
a  reed,  a  column  of  air,  or  any  other  sound-producing  body,  is  vi- 
brating as  a  whole  and  thus  producing  its  fundamental  sound,  it  is  at 
the  same  time  generally  vibrating  in  parts  also,  which  produce  the 
overtones.  If  only  the  larger  parts  are  vibrating,  as  the  halves,  thirds, 
or  fourths,  or  if  the  sounds  of  these  predominate,  we  can  now  see 
that  these  would  harmonize  with  the  fundamental  sound  and  with  one 
another,  and  blending  all  together  they  would  produce  a  pleasing 
sound.  These  lower  overtones  are  therefore  called  harmonics.  It  is 
to  them  that  we  owe  the  pleasing  effect  of  a  sweet  voice,  of  a  lower 
or  middle  key  of  a  good  piano,  or  of  any  other  single  note  that  we 

1  Mayer's  Sound,  pp.  174,  175. 
14 


158 


NATURAL   PHILOSOPHY. 


recognize  as  pleasant.  But  if  the  overtones  are  wholly  or  mainly 
the  vibrations  of  the  sevenths,  eighths,  ninths,  etc.,  they  will  not 
harmonize  with  the  fundamental  note  or  with  one  another,  and  the 
result  is  a  harsh  sound.  It  is  these  that  make  a  harsh  voice,  scraping 
on  a  violin,  and  other  unpleasant  musical  sounds  so  disagreeable. 

Experiment  80. — Strike  middle  C  of  a  pjano  two  or  three  times,  so 
that  you  can  recognize  its  sound  when  you  hear  it  again,  then  press 
it  down  gently  so  as  to  make  no  sound, "and  hold  it  there,  thus  keep- 
ing the  damper  oif  the  wire.  Now  strike  the  C,  one  octave  below, 
vigorously,  and,  after  holding  that  key  down  for  three  or  four  seconds, 
let  it  rise  again.  Its  damper  stops  its  sound  at  once,  but  you  now 
hear  a  faint  sound,  which  you  recognize  as  that  of  middle  C,  which 
you  are  holding  down.  When  you  struck  lower  C  it  vibrated  in 
halves,  besides  its  vibration  as  a  whole.  And  the  vibrations  of  these 
halves  set  the  wire  of  middle  C  to  vibrating.  In  the  same  way  you 
may  hear  the  sympathetic  vibrations  of  Gr  above  middle  C  produced 
by  the  thirds  of  the  lower  C.  And  possibly  its  fourths  may  set  C, 
two  octaves  above  it,  in  vibration. 

Their  overtones  also  have  an  effect  upon  the  harmony  or  discord  of 
two  notes.  To  make  them  harmonious  these  two  must  make  very 
rapid  beats  with  each  other  and  with  the  fundamental  notes. 

249.  The  Human  Ear. — This  organ  is  shown  in  Fig.  147. 

The  end  of  the  tube 
leading  in  from  the 
outer  ear  is  entirely 
closed  by  a  thin 
membrane  called  the 
tym'panum.  Behind 
this  is  a  small  cavity 
called  the  drum  of 
the  ear.  This  cavity 
is  connected  with 
the  back  part  of  the 
mouth  by  the  Eusta- 
chian  (yu-sta'ke-an) 
tube.  A  chain  of  four 
FIG.  H7.— HUMAN  EAR.  very  small  bones 

stretches  across  the 

drum  from  the  tympanum  to  another  smaller  membrane 
that  covers  an  opening  into  the  labyrinth.  This  labyrinth 
is  a  small,  curiously-shaped  cavity  in  the  solid  bone  of  the 


SOUND.  159 


skull,  and  is  filled  with  a  watery  fluid.  The  nerve  of  hear- 
ing runs  from  the  brain  to  the  labyrinth,  and  there  divides 
up  into  thousands  of  microscopic  branches,  which  stick  out 
like  bristles  from  the  sides  of  the  labyrinth  into  the  liquid 
which  fills  it. 

250.  How  we  Hear. — The  sound-vibrations  enter  the  ear, 
strike  the  tympanum,  and  set  it  in  vibration.  Its  vibra- 
tions are  carried  across  the  drum  of  the  ear  by  the  chain 
of  little  bones,  and  also  by  the  air  there,  and  set  the  mem- 
brane covering  the  openings  into  the  labyrinth  into  vibra- 
tion ;  and  this  communicates  its  vibrations  to  the  liquid 
within.  The  tiny  bristles  which  project  into  the  liquid 
are  of  different  lengths  and  thicknesses,  and  it  is  supposed 
that  these  are  tuned  each  to  a  different  pitch,  and,  in  all, 
to  all  the  pitches  that  are  audible.  It  is  likely,  then, 
that  the  waves  in  the  liquid  which  are  produced  by  sound 
of  a  certain  pitch  set  to  vibrating  the  bristle  which  is 
tuned  to  the  same  pitch,  and  that  the  nerve-thread  at- 
tached to  this  bristle  conveys  this  impression  to  the  brain 
and  to  the  mind.  When  the  sound  contains  overtones  as 
well  as  the  fundamental,  each  element  of  the  sound  must 
set  in  motion  the  bristle  tuned  to  its  pitch,  and  the  com- 
bined impressions  of  these  give  us  the  true  impression  of 
the  sound. 

Exercises. — 1.  Why  does  touching  a  call-bell  with  your  finger 
silence  it? 

2.  There  is  helieved  to  be  no  atmosphere  of  any  kind  on  the  moon  : 
would  this  have  any  effect  on  sounds  there  ? 

3.  Your  pulse  probably  beats  about  80  times  per  minute.    Suppose 
that  on  a  day  when  the  temperature  is  at  the  freezing-point  you  count 
five  beats  of  your  pulse  after  you  see  the  escaping  steam  of  an  engine- 
whistle,  and  before  you  hear  its  sound  :  how  far  off  is  the  engine  ? 
Ans.  4087£  feet. 

4.  Suppose  that  on  a  summer  day,  when  the  thermometer  stands 
at  80°,  you  count  four  beats  of  your  pulse  between  a  flash  of  light- 
ning and  the  first  sound  of  the  thunder  :  how  far  off  is  the  lightning  ? 

5.  A  leader  of  a  room  full  of  singers  is  at  one  end  of  the  room, 
which  is  60  feet  long.     If  the  temperature  of  the  room  is  68°  (which 
is  about  what  it  ought  to  be),  how  much  will  the  words  of  the  singers 
on  the  back  seat  seem  to  the  leader  to  be  behind  his  own  ?    Ans.  •££§ 
seconds. 


160  NATURAL  PHILOSOPHY. 


6.  What  is  the  temperature  of  the  air  when  the  velocity  of  sound 
is  1150  feet  per  second  ?     Ans.  92°. 

7.  Until  recently  the  velocity  of  sound  was  always  given  as  1142 
feet  per  second  :  what  must  have  been  the  temperature  when  that 
result  was  obtained  ? 

8.  How  far  off  is  a  barn  when  the  echo  of  your  voice  comes  back  to 
you  after  you  have  counted  three  beats  of  your  pulse,  the  tempera- 
ture being  at  60°  ? 

9.  The  bell  in  the  clock-tower  at  Westminster  Abbey,  London,  is 
300  feet  above  the  ground  :  find  the  time  sound  takes  to  pass  from 
the  bell  to  a  point  on  the  ground  400  feet  from  the  foot  of  the  tower, 
the  temperature  being  the  same  as  in  the  last  problem  ?     Ans.  f  f  $ 
seconds. 

10.  Could  you  set  your  watch   to  the  second  by  the  striking  of  a 
tower-clock  some  distance  off?    Why  will  a  large  company  of  singers 
keep  better  time  if  their  leader  beats   time  instead  of  leading  them 
with  his  voice?   How  will  it  affect  the  drill  of  a  long  line  of  soldiers  if 
the  officer  gives  his  commands  while  standing  at  one  end  of  the  line? 

11.  How  much  louder  is  a  sound  50  yards  from  its  origin  than  at  a 
point   70  yards   distant  ?      Ans.  As    ^^  :  ¥^,  or    as   4900 :  2500. 
Therefore  ff-  as  loud. 

12.  How  much   louder  will  a   sound  be  40  yards  than  90  yards 
away? 

13.  What  is  the  length  of  each  wave  of  the  lowest  sound  that  we 
can  hear  ?  of  the  highest  ? 

14.  Give  the  difference  between  musical  and  non-musical  sounds. 

15.  Explain  the  meaning  and   causes  of  loudness,  pitch,  and  char- 
acter. 

16.  Give  an  example  of  two  musical   sounds  that  agree  in  one  of 
these  characteristics  only ;  of  two  others  agreeing  in  two  of  them. 

17.  A  certain  string  vibrates  100  times  per  second  :  find  the  number 
of  vibrations  of  another  string  which  is  twice  as  long  and  weighs 
four  times   as   much  per  foot  and  is  stretched  by  the  same  force. 
Ans.  25. 

18.  A  musical  string  vibrates    400  times  per  second :  what  takes 
place  when  the  string  is  lengthened  or  shortened  without  altering  the 
tension  ?  when  the  tension  is   made  greater  or  less  without  altering 
the  length? 

19.  A  tuning-fork  vibrates  over  a  jar  15  inches  deep,  and  a  strong 
resonance  is  produced :  what  is  the  rate  of  the  fork's  vibrations  if  the 
temperature  is  such  that  sound  travels  1120  feet  per  second? 

20.  If  do  vibrates  264  times  per  second,  how  many  vibrations   in 
mi  above  it  ?  in  sol  ?  in  the  upper  do  ? 

21.  If  do  vibrates  264  times  per  second,  how  many  vibrations  pro- 
duce re,  si,  and  fa  in  the  octave  below  ? 

22.  Draw  on  the  blackboard  a  line  30  inches  long,  and  above  it 
draw  lines  of  the  right  proportions  to  represent  strings  which  would 
give  the  notes  of  the  octave  above. 

23.  Middle  C  of  a  piano  vibrates  272  times  per  second.    In  a  seven- 
octave  piano  the  lowest  key  is  the  fourth  A  below  middle  C,  and  the 
highest  is  the  fourth  A  above  it :  what  are  the  rates  of  vibrations  of 
these  two  keys  ? 


SOUND. 


24.  In  a  seven-and-one-third-octave  piano  the  lowest  key  is  the 
same  as  before,  but  the  highest  is  the  fourth  C  (four  octaves)  above 
middle  C  :  how  many  more  vibrations  per  second  will  the  highest  key 
of  this  piano  make  than  the  highest  one  of  the  "other  ? 

25.  If  re  is  produced  by  216  vibrations  per  second,  how  many  will 
produce  do  below  ?  re  below  ?  la  above  ? 

26.  Over  how  many  octaves  does  the  range  of  human   hearing 
extend  ? 

27.  How  many  beats  per  second  will  there  be  when  middle  C  and 
G  above  are  sounding  together  on  a  piano  ?  how  many  when  B  above 
is  sounded  with  middle  C  ? 

28.  If  corresponding  keys  towards  the  upper  end  of  the  key-board 
be  sounded  together,  will  the  beats  be  the  same  as  in  last  problem  ? 
How  will  it  be  if  they  are  taken  in  the  lower  end  of  the  key-board? 


162  NATURAL  PHILOSOPHY. 


CHAPTEE  YI. 

LIGHT. 
I.-THROUGH  UNIFORM  MEDIA. 

251.  Sources  of  Light. — Light  comes  to  us  from  the  sun 
by  day  and  from  the  moon  and  stars  by  night.     It  is  pro- 
duced on  the  earth  by  combustion,  by  friction,  by  elec- 
tricity, and  by  phosphorescence.     Light  from  combustion 
is  familiar  in  all  fires.     Light  from  friction  may  be  seen  by 
rubbing  two  pieces  of  white  sugar  together  in  the  dark. 
The  light  from  meteors  (shooting-stars)  is  produced  by  the 
friction  of  small  bodies  moving  with  great  velocity  through 
the  atmosphere.     Light  from  electricity  is  visible  when  a 
cat  is  stroked  vigorously  in  the  dark.     The  lightning  and 
the  aurora  are  forms  of  this.     Light  from  phosphorescence 
is  often  seen  in  decayed  wood,  in  "luminous  paint," — a  salt 
of  calcium  which  glows  when  taken  from  a  light  place  to 
a  dark  one, — and  in  a  fire-fly. 

Astronomy  tells  us  that  the  sun  is  one  of  the  stars,  and 
that  the  moonlight  is  only  reflected  sunlight.  Hence  we 
may  say  that  we  have  one  celestial  source  of  light, — the 
stars, — and  four  terrestrial  sources, — combustion,  friction, 
electricity,  and  phosphorescence. 

252.  Cause  of  Light.— In   all   these  cases  the  light  is 
produced  in  the  same  way.      The  particles  of  the  body 
from  which  the  light  comes  are  put  in  extremely  rapid 
vibration.     The  surrounding  ether  catches  up  these  vibra- 
tions and  carries  them  along  like  waves  in  water  till  they 
reach  the  eye  of  the  observer,  and  the  sensation  produced 
is  light. 


LIGHT.  163 


253.  Light-Waves. — Light-waves  lie  across  the  direction 
in  which  the  light  travels.     If  we  suppose 

the  ray  of  light  to  be  moving  perpendicu- 
larly to  this  page,  the  particles  of  ether 
vibrate  up  and  down  in  ab,  across  in  cdt 
and  diagonally  at  all  angles  in  ef,  etc. 

The  water-wave  moves  horizontally,  while  FIO.  us  — CROSS-SEC- 
TION or  RAY  OF  LIGHT. 
its  particles  vibrate    up  and    down   only. 

The  method  of  vibration  of  the  sound-wave  has  already 
been  explained.  The  light-wave  is  different  from  either 
of  these.  Its  particles  move  transversely  to  the  motion  of 
the  wave  in  all  directions.  Its  vibrations  are  very  minute 
and  very  rapid.  When  a  piece  of  iron  is  heated,  its  par- 
ticles are  set  into  vibration.  At  first  this  vibration  is  slow, 
and  only  affects  the  nerves  sensitive  to  heat.  But  when 
the  temperature  is  raised  so  that  about  400  million  million 
of  them  occur  in  a  second,  a  red  glow  begins  to  show  itself. 
Light  is  given  out.  When  the  temperature  is  further 
raised  so  that  the  number  of  vibrations  is  nearly  doubled, 
the  iron  is  white-hot.  The  intensity  of  the  light  is  greatly 
increased.  From  40,000  to  70,000  of  these  waves  are  in  a 
linear  inch. 

254.  Light  moves  in  Straight  Lines. — These  vibrations 
are  carried  forward  in  straight  lines  so  long  as  they  do  not 
meet  with  any  change  in  the  substance  through  which 
they  pass.     We   always  recognize  this.     We  assume   an 
object  to  be  in  the  direction  in  which  we  see  it, — that  the 
light  by  which  we  see  it  carries  the  impression  to  the  eye 
in  a  straight   line.      We  can  test  the   same  fact  by  an 
experiment. 

Experiment  81. — Arrange  three  cards  by  fastening  them  to  blocks 
so  that  they  will  stand  upright  on  a  table.  Pierce  a  small  hole  in 
each  card,  and  place  them  so  that  a  stretched  string  will  go  straight 
through  all  the  holes.  Now  put  a  lamp  in  front  of  the  end  hole.  It 
will  shine  through  all.  But  if  any  of  the  cards  be  moved  so  that  the 
holes  are  not  in  a  straight  line,  the  light  will  not  shine  through. 

Experiment  82. — Darken  a  room,  and  make  a  small  hole  in  a  shut- 
ter opposite  a  white  wall.  Over  this  paste  a  piece  of  paper  in  which 


164 


NATURAL  PHILOSOPHY. 


a  large  pin-hole  is  pierced.  The  outside  landscape  will  be  projected 
on  the  wall  inverted,  for  all  the  rays  will  cross  at  the  opening.  Kays 
from  a  will  move  in  straight  lines  to  «',  and  rays  from  b  to  b/. 


FIG.  149.— IMAGE  THROUGH  A  SMALL  HOLE. 


T" 

nl'" 


FIG.  150.— LIGHT  MOVES 
IN  STRAIGHT  LINES. 


Experiment  83. — Hold  a  candle  in  front  of  a  card  in  which  a  pin- 
hole  is  pierced.  The  candle  will  be  seen  inverted 
on  a  small  screen  held  beyond  the  hole. 

Experiment  84. — Have  made  in  a  a  temporary 
window-shutter  a  number  of  small  openings  of 
different  shapes,  and  let  the  sunshine  through  into 
the  room.     Keceive  the  image  from  them  on  a 
screen  placed  at  a  distance  from  the  holes.    These 
images  will  all  be  round,  not  the  shape  of  the  holes. 
They  are  images  of  the  round  sun. 
The  same  may  be  seen  in  the  light  patches  on  the  ground  under  a 
tree,  formed  by  the  passage  of  sunlight  through  the  small  openings 
of  the  foliage. 

255.  Opaque,  Transparent. — When  a  body  allows  light  to 
pass  through  it,  it  is  said  to  be  transparent ;  when  it  does 

'not,  it  is  said  to  be  opaque. 

Name  several  opaque  and  several  transparent  substances. 

256.  Shadows. — Shadows  are  a  result  of  the  motion  of 


LIGHT. 


165 


light-waves  in  straight  lines.     If  an  opaque  body  be  placed 


FIG.  151.— IMAGE  BY  PASSING  LIGHT  THROUGH  A  SMALL  HOLE. 

between  a  source  of  light  and  the  wall,  a  dark  place  is 
shown  on  the  wall, 
which  is  due  to  the 
fact  that  the  light 
which  would  other- 
wise fall  on  it  is  cut 
off  by  the  opaque 
body. 

Experiment  85. — 
Stretch  a  string  from  the 
source  of  light  touching 

the  edge  of  the  shadow  ;  FlQ>  ^.-SHADOW. 

it  will  touch  the  edge  of 
the  body. 

Experiment  86.— Make  the  body  a  square,  and  place  it  exactly  half- 
way between  the  light  and  the  wall.  Measure  the  shadow.  Its  side 
will  be  twice  the  side  of  the  square,  and  hence  its  area  will  be  four 
times  that  of  the  square. 


166  NATURAL   PHILOSOPHY. 

• 

257.  Law  of  Light-Variation. — This  last  experiment  ex- 
plains an  important  law.     The  light  which  would  have 
been  spread  over  the  space  occupied  by  the  shadow  now 
is  collected  on  the  square,  and  therefore  covers  only  one- 
fourth  the  space.     Hence  it  is  four  times  as  intense  on  the 
screen  as  at  the  wall.     The  wall  is  twice  as  far  from  the 
light  as  the  square  is,  and  the  intensity  is  only  one-fourth 
as  great.     Were  the  wall  three  times  as  far  away,  the  in- 
tensity of  the  light  would  be  only  one-ninth  as  great.     The 
general  law  is,  Light  diminishes  as  the  square  of  the  distance 
increases. 

258.  Photometry, — We  can  compare  the  relative  intensi- 
ties of  two  lights  by  the  aid  of  this  law. 

Experiment  87. — Place  an  opaque  body  in  front  of  a  wall,  and 
arrange  the  lights  so  that  the  two  shadows  shall  be  side  by  side. 


FIG.  153. — PHOTOMETRY. 


Move  one  of  the  lights  backward  or  forward  till  the  shadows  are  of 
the  same  intensity  of  darkness.  The  shadow  from  a  is  still  lit  up  by 
&,  and  the  shadow  from  b  by  a.  If  the  shadows  are  equally  bright, 
the  intensities  of  the  light  given  by  the  two  bodies  at  the  wall  are  the 


LIGHT. 


167 


same.     Now  measure  the  distance  of  each  light  from  the  wall.     The 
squares  of  these  distances  will  be  the  relative  intensities  of  the  lights. 

259.  Umbra  and  Penumbra, — If  the  source  of  light,  instead 
of  being  small,  is  of  considerable  size,  we  shall  find  that  the 


FIG.  154.— UMBRA  AND  PENUMBRA. 

shadow  is  not  definite  in  outline,  but  gradually  shades  out. 
The  cause  of  this  is  shown  in  Fig.  154. 

The  portion  directly  behind  the  intercepting  object  does 
not  receive  any  light  from  the  source,  and  is  called  the 
umbra.  The  shaded  portion  on  each  side  of  this  receives 
light  from  part  of  the  source  only,  the  part  increasing  as 
we  depart  from  the  umbra,  and  is  called  the  penumbra. 

The  penumbra  gives  to  the  shadows  of  bodies  a  softness 
of  outline  which  they  do  not  receive  when  the  source  of 
light  is  very  small.  Moreover,  as  this  penumbra  increases 
in  size  as  the  distance  from  the  body  increases,  this  soft- 
ness shows  itself  more  conspicuously  as  we  move  the  body 
away  from  its  shadow. 

Experiment  88. — Throw  a  shadow  on  a  wall  by  a  body  close  to  it. 
Move  the  body  away,  and  notice  the  change  in  distinctness  of  shadow. 

260.  Velocity  of  Light. — For  a  long  time  it  was  supposed 
that  light  was  propagated  instantaneously.  Galileo  took 
a  lantern  to  the  top  of  a  mountain,  and  had  an  assistant  on 
the  top  of  another,  where  there  were  no  intervening  objects. 
He  cut  off  the  light  suddenly,  and  told  his  assistant  to  cut 


168 


NATURAL  PHILOSOPHY. 


his  off  as  soon  as  he  missed  the  light  from  Galileo's.  As  he 
did  not  notice  that  it  took  any  time  between  the  extin- 
guishment of  the  two  lanterns,  he  concluded  that  the  light 
took  no  time  to  travel.  He  erred  only  in  this,  that  the 
time  was  too  small  to  be  detected  by  such  rude  means. 

261.  Velocity  obtained  from  Jupiter's  Moons.— The  first  idea 

that  light  had  velocity  was  gained  by  examination  of  Jupiter's  satel- 
lites. In  the  figure,  TOY 
represents  the  orbit  of  the 
earth  around  the  sun,  and 
JJ  a  part  of  Jupiter's 
orbit.  Jupiter  casts  a 
shadow  on  the  side  away 
from  the  sun,  and  into  this 
shadow  plunge  his  little 
moons  in  their  revolution 
about  him.  The  time  of 
these  eclipses  can  be  cal- 
culated in  advance,  and  it 
has  been  found  that  when 
the  earth  is  at  T'it  appears 
to  us  earlier  than  when 
the  earth  is  at  T.  The 
reason  of  this  is  that  the 
light  has  to  travel  the  dis- 
tance from  T'  to  T,  the 
diameter  of  the  earth's 
orbit,  farther  in  one 
case  than  in  the  other. 
The  difference  in  time 
amounts  to  about  16J 
minutes.  As  we  know 
that  the  diameter  of  the 
earth's  orbit  is  about 

185,000,000  miles,  we  can  readily  calculate  the  velocity  of  light. 

Thus,  16^  minutes  =  990  seconds : 
185,000,000  miles -=-990=:  187,000  miles,  nearly,  per  second. 

262.  A  Better  Method. — A  still  more  accurate  determination  can 
be  obtained  by  the  following  method  :  a  is  a  mirror  which  can  re- 
volve about  a  vertical  axis,  ef.     &  is  a  stationary  mirror,    g  is  an 
opaque  body  containing  a  narrow  slit.     Sunlight  is  thrown  through 


FIG.  155, 


-VELOCITY  OF  LIGHT  BY  ECLIPSES  OF  JUPI- 
TER'S SATELLITES. 


LIGHT. 


169 


this  slit  so  that  it  falls  on  the  mirror  a,  and  is  reflected  to  6,  and  back 
again  to  a.  If  a  has  not 
moved,  the  light  would  be 
again  reflected  directly  to  the 
flit  in  g.  But  a  may  be 
made  to  revolve  with  great  ra- 
pidity, and  during  the  minute 
time  that  the  light  has  been 
travelling  from  a  to  b  and 
back  again,  the  mirror  has 
changed  its  position  a  little, 
so  that  the  light  is  now  thrown 
to  some  other  point,  as  h. 
Knowing  the  velocity  of  the 
mirror  and  the  distance  of  h 
from  the  slit,  it  is  possible  to 
calculate  the  time  required  in  FIG.  156 —FOR  FINDING  THE  VELOCITY  OF  LIGHT. 
passing  twice  between  a  and 
b.  Now  measuring  the  distance,  the  velocity  of  light  is  found. 

The  best  results  obtained  for  the  velocity  of  light  are 
299,940  kilometres,  or  186,380  miles,  per  second. 

Exercises. — 1.  A  board  1  foot  square  is  held  between  a  point  of 
light  and  a  wall,  parallel  to  the  wall.  If  2  feet  from  the  light  and  4 
feet  from  the  wall,  what  is  the  size  of  the  shadow? 

2.  A  coin  casts  a  shadow  on  a  wail  to  which  it  is  not  parallel :  what 
is  the  shape  of  the  shadow  ? 

3.  A  lamp  8  feet  from  a  wall  throws  a  shadow  which  is  just  as 
bright  as  that  thrown  by  a  candle  2  feet  from  the  wall :    compare  the 
light  of  the  two. 

4.  Light  requires  about  3  J  years  to  come  from  the  nearest  star : 
how  far  is  it  away  ? 

5.  Does  the  fact  that  we  see  the  stars  prove  that  they  are  in  existence 
at   ae  present  time  ? 

i.  How  long  would  it  take  light  to  go  to  the  moon  ?  how  long 
a.ound  the  earth  ? 

II.— REFLECTION. 

263.  Reflection. — When  light  falls  on  a  smooth  surface 
which  it  cannot  penetrate,  it  is  turned  back,  or  reflected. 

Experiment  89. — Allow  sunlight  to  shine  into  a  dark  room  through 
a  small  hole.  The  beam  l  will  be  visible  by  lighting  up  the  particles 

1  This  is  better  arranged  by  means  of  a  heliostat,  which  reflects  the 
light  into  the  room.      A  sample  one  is  described,  together  with  a 
H  15 


170 


NATURAL  PHILOSOPHY. 


of  dust  which  are  always  floating  in  the  air.  It  can  be  in  this  and 
other  cases  made  still  more  evident  by  smoke  from  heavy  brown 
paper.  Let  it  fall  perpendicularly  on  a  mirror.  The  beam  is  turned 
directly  back  on  its  track.  Turn  the  mirror  45°,  the  light  goes  off 
at  right  angles  to  its  former  course. 

Experiment  90. — Allow  the  beam  of  light  from  the  sun  or  a  lamp 
h  to  shine  through  a  hole  in  a  card 

at  dj  to  fall  on  a  mirror  at  6,  and 
J   to  be  reflected  on  another  card  at  e. 
n   Make  a  hole  at  e  at  the  same  height 
above  c  that  d  is  above  a.     Look 
through  the  hole  at  e  and  see  the 
light  reflected  from  b.      Mark  the 
exact  point  where  the  light  falls  at 
b.     Now  measure  ab  and  be.     They 
will  be  equal.  We  can  readily  prove 
from  this  by  geometry  that  the  angle  dbh  is  equal  to  the  angle  ebh. 

264.  Incident   and  Reflected  Rays.— In  Fig.  157,  db  is 
said  to  be  the  incident  ray,  and  be  the  reflected  ray ;  dbh  is 
the  angle  of  incidence,  and  ebh  the  angle  of  reflection. 

265.  Law  of  Reflection. — The  general  law  of  reflection  is 
that  the  angle  of  incidence  is  equal  to  the  angle  of  reflection. 

266.  Principle  of  Mirrors. — We   may  understand  from 


FIG.  157. — REFLECTION  OF  LIGHT. 


FIG.  158.— PRINCIPLE  OF  MIRRORS. 


this  and  from  Fig.  158  how  it  is  that  we  see  objects  in  a 
looking-glass.     Objects  are  seen  in  the  direction  in  which 


number  of  interesting  experiments  to  be  performed  with  it,  in  Light, 
by  Mayer  and  Barnard. 


LIGHT,  171 


the  rays  of  light  from  them  enter  the  eye.  The  glass  turns 
these  rays  back,  making  the  same  angle  with  the  perpen- 
dicular that  they  had  before,  and  we  therefore  seem  to  see 
them,  back  of  the  glass,  the  same  distance  from  it  that 
they  are  in  reality  in  front  of  it,  but  inverted  right  and  left. 
The  image  is  not  real;  it  is  an  optical  delusion.  Such 
images  are  said  to  be  apparent  images. 

267.  Natural  Objects. — It  is  by  the  aid  of  reflected  light 
that  we  see  most   natural  objects.     When  the  object  is 
smooth,  as  a  mirror,  the  light  is  reflected  in  parallel  rays, 
and  we  notice  only  the  glare ;  but  when  its  surface  is  rough, 
such  as  that  of  a  book  or  wall  or  landscape,  the  reflected 
light  is  diffused  in  all  directions,  and  the  object  is  seen  by  it. 

268.  Multiple  Images. — We  sometimes  see  more  than  one 
image  of  an  object. 

Experiment  91. — Take  a  mirror  out  into  the  starlight,  and  see  the 
reflection  of  a  bright  star  or  planet  at  an  oblique  angle.  The  star 
will  seem  to  be  attended  by  a  small  companion.  This  is  due  to  the 
reflection  from  the  front  face  of  the  glass,  as  shown  in  Fig.  159.  One 


FIQ.  159.— DOUBLE  IMAGE.  FIG.  1GO.— IMAGES  BY  Two  MIRRORS. 

reflection  comes  to  us  from  the  silvered  back  of  the  mirror,  the  other, 
the  fainter  one,  comes  from  the  front  face. 

If  two  mirrors  are  inclined  to  each  other,  quite  a  number  of  images 
may  be  seen.  Fig.  160  shows  one  case  of  this. 

Fig.  161  shows  the  reason  of  this.    If  p  is  the  candle,  and  e  the  eye 


172 


NATURAL   PHILOSOPHY. 


of  the  observer,  he  sees  one  object  at  p/  by  direct  reflection  from  ab, 


FIG.  161.— IMAGES  BY  Two  MIRRORS. 

one  at  p"  by  reflection  from  be,  and  one  at  p"r  by  reflection  first  from 
ab  and  then  from  be. 

269.  The  Kaleidoscope. — The  kaleidoscope  is  composed  of  three 
mirrors  inclined  at  angles  of  60°  to  one  another,  and  arranged  along 

the  whole  length  of  a  tube.  At  one  end  the  person 
puts  his  eye  and  sees  a  number  of  colored  glasses 
at  the  other  end,  reflected  and  re-reflected  from 
mirror  to  mirror,  thus  causing  the  appearance  of 
symmetrical  figures  of  great  beauty.  Fig.  162 
shows  a  cross-section.  The  circle  represents  a 
tube,  which  may  be  of  pasteboard.  The  straight 

FXG.  ^.-CROSS-SECTION  lines  are  strif  of  glass  (clear  glass  will  answer) 

OF  THE  KALEIDOSCOPE,     placed  along  it.    An  eye-hole  must  be  at  one  end, 

and  in  the  other  some  ground  glass  or  oiled  paper, 

or  some  semi-transparent  substance.     On  this  a  few  irregular  pieces 

of  broken  colored  glasses  are  scattered.     These  are  kept  in  the  bottom 

of  the  tube  by  a  piece  of  clear  glass. 

The  ingenious  student  can  make  a  kaleidoscope  for  himself. 

270.  Concave  Mirrors. — Concave  mirrors  produce  a  dif- 
ferent effect  from  plane  mirrors.     Let  ab  be  an  arc  of  a 

circle,  and  cd  the  direction  of  an  in- 
cident ray  of  light.  The  perpendic- 
ular to  the  surface  will  always  pass 
through  the  centre,  /,  of  the  arc, 
fA  and  the  reflected  ray  will  be  in  the 
direction  de,  making  cdf=edf.  Any 

FIG.  163.-PRINCIPAL  FOCUS,  other  ray,  as  ght  parallel  to  bd,  will 
be  reflected  in  the  line  he,  which  will 

meet  de  in  some  point  e.     Hence  the  effect  of  a  concave 


LIGHT, 


173 


mirror  is  to  converge  the  rays  of  light,  or  to  make  diver- 
gent rays  less  divergent. 

271.  Principal  Focus. — The  point  to  which  the  parallel 
rays  converge  is  called  the  principal  focus,  and  is  midway 
between  /  and  k. 

272.  Parabolic  Mirror. — If  ab  is  a  circle,  all  parallel  rays 
will  not  meet  in  exactly  one  point.     In  order  for  this,  ab 
must  be  a  curve  called  a  parabola  (see  page  43).     Also,  if 


FIG.  164.— CONJUGATE  Foci. 


a  light  be  placed  at  e,  the  rays,  after  reflection,  will  all  be 
parallel.  This  principle  is  used  in  making  reflections  for 
lanterns.  The  light  is  so  placed  inside  the  parabolic  mirror 


FIG.  165.— CONJUGATE  Foci. 

that  all  rays  which  strike  it  are  reflected  forward  in  par- 
allel or  nearly  parallel  lines.  The  principle  is  also  used  in 
the  mirrors  of  reflecting  telescopes,  where  parallel  rays 
frqm  the  heavenly  bodies  are  brought  to  a  focus,  near  which 
the  eye  is  placed.  If  the  rays  do  not  come  in  parallel,  but 
diverge  from  some  point  as  S  (Figs.  164,  165),  they  will 
converge  to  some  other  point  as  s.  If  they  diverge  from  s, 
they  will  converge  to  S.  S  and  s  are  called  conjugate  foci. 
273.  Images  by  a  Concave  Mirror,  Let  ab  be  an  object 


174 


NATURAL   PHILOSOPHY. 


placed  farther  from  the  mirror  than  the  centre,  c.  Now, 
whenever  any  bundle  of  rays  pro- 
ceeding from  a  single  point  are 
brought  together  at  another  point, 
an  image  is  there  formed.  All 
rays  from  a  will  meet  in  a  point 
at  a'.  This  point  can  be  most 
easily  found  by  drawing  the  par- 
allel ray,  ag,  and  its  direction  of 
reflection  through  the  principal 
focus,  gfa' ;  also  the  ray,  ah,  through  the  centre,  which  is 
reflected  directly  back  towards  the  centre.  The  intersection 
a'  of  go!  and  a'h  is  tne  image  of  a.  Similarly,  the  light 


FIG.  166.— IMAGES  BY  CONCAVE 
MIRROR. 


FIG.  167.— IMAGE  BY  CONCAVE  MIRROR. 


from  b  will  be  focussed  at  V,  and  all  points  of  ab  will  have 
corresponding  points  in  a'b'.     We  shall  then  have  a  real 


LIGHT.  1 75 


image,  inverted  and  smaller  than  the  object.     By  holding 
a  piece  of  white  paper  at  a'b',  we  can,  if  it  does  not  cut 


FIG.  168.— IMAGE  BY  CONCAVB  MIRRORS. 

off  too  many  of  the  rays  which  would  fall  on  the  mirror 
from  ab,  see  the  inverted  image. 

If  the  object  be  placed  at  a'bf,  the  image  will  be  formed 
inverted  and  enlarged  at  ab.  (Fig.  166.) 

Exercises. — Show  by  construction  that  (a)  if  the  object  be  at  the 
centre  the  image  will  be  at  the  centre  inverted  ;  (b)  if  the  object  be 
at  the  focus  there  will  be  no  image ;  (c)  if  the  object  be  between  the 
focus  and  the  mirror  there  will  be  an  image  behind  the  mirror,  ap- 
parent, erect,  and  magnified. 

Experiment  92. — Take  a  glass  concave  mirror,  or,  if  this  cannot 
be  had,  a  lantern-reflector,  and  verify  the  above  in  all  the  cases, — 

1.  By  looking  in  the  mirror  at  varying  distances  ; 

2.  By  placing  a  candle  at  different  distances  from  the  mirror  and 
catching  the  image  on  a  screen. 

274.  Convex  Mirrors. — Convex  mirrors  cause  parallel 
rays  to  diverge  from  a  point  behind  the  mirror,  which  is 
the  principal  focus.  The  images  from  a  convex  mirror  are 
always  behind  the  mirror,  apparent,  erect,  and  smaller  than 
the  object. 

Experiment  93. — With  a  convex  mirror  of  glass  or  "  tin"  examine 


176  NATURAL   PHILOSOPHY. 


the  truth  of  these  statements  by  looking  into  it  from  varying  dis- 
tances. 

275.  Diffusion  of  Light. — The  sun  shines  on  the  air,  and 
the  little  particles  of  dust  and  vapor  which  it  contains  re- 
flect the  rays  in  all  directions.     This  is  the  reason  that 
sunlight  gets  into  our  rooms  and  under  trees.     This  brings 
light  to  our  eyes  and  enables  us  to  see  objects  upon  which 
the  sun  does  not  shine  directly. 

276.  Twilight. — Twilight  is  produced  by  a  similar  cause. 

Even  when  the  sun  is  be- 
low the  horizon  some  of 
its  rays  are  reflected  to  us 
by  invisible  particles  in 
the  atmosphere.  As  it  gets 
farther  down  it  shines  only 
on  the  upper  layers,  and 
so  the  day  gradually 

FIG.  169.— DIFFUSION  OF  LIGHT.  changes  into  night. 

Objects  are  seen  by  the 

light  which  they  diffuse.  If  the  surface  is  very  smooth, 
the  light  is  reflected  in  parallel  lines,  and  a  glare  is  pro- 
duced. If  not,  the  light  is  reflected  in  all  directions,  and 
the  features  of  the  object  are  brought  out. 

Exercises. — 1.  Shall  we  notice  double  reflection  when  we  look  per- 
pendicularly on  a  mirror  ?  Draw  a  figure  to  show  that  the  two 
images  will  be  farther  apart  the  more  obliquely  we  see  the  object 
reflected  from  the  mirror. 

<          2.  Draw  a  diagram  to  show  that  an 

^f  9     object  seen  between  two  parallel  plane 

"~ .     mirrors  will  have  its  image  several  times 

TIG.  170.  multiplied. 

3.  Draw  a  diagram  to  show  that  a  per- 
son can  see  himself  in  a  mirror  half  as  long  as  himself. 

4.  If  the  sun,  93,000,000  miles  away,  and  an  electric  light,  20  feet 
away,  cast  shadows  of  the  same  intensity,  how  many  times  brighter 
is  the  sun  than  the  electric  light  ? 

5.  If  there  were  no  atmosphere  surrounding  the  earth,  why  would 
the  stars  look  like  points  of  light  in  a   black  sky  ?  why  would  all 
shadows  be  perfectly  black  ?  Do  we  see  any  rays  of  light  except  such 
as  enter  the  eye  ?  if  not,  how  do  we  see  a  beam  of  light  pass  through 
a  dark  room  ? 


LIGHT. 


177 


III.-REFRACTION. 

277.  Refraction, — When  light  passes  obliquely  from  one 
transparent    substance 

to  another,  as  from 
air  to  clear  water,  it  is 
turned  from  its  course, 
or  refracted. 

278.  Law  of  Refrac- 
tion.— This    refraction 
is   shown   in  Fig.  171. 
The  course  of  the  beam 
will   be   the   same 
whether  it  passes  from 


FIG.  171.— RKFRACTION. 

the  air  into  the  water  or  from  the  water  into  the  air. 
The  rule  is,  when  light  passes  from  a  medium  into  a  denser 
medium,  it  is  turned  towards  the  perpendicular  to  its  surface  ; 
when  it  passes  into  a  rarer  medium,  it  is  turned  away  from  the 
perpendicular  to  its  surface. 


FIG.  172. — COIN  MADE  VISIBLE  BY  REFRACTION. 
Experiment  94. — Place  a  coin  on  the  bottom  of  a  basin  so  as  to  be 


178 


NATURAL  PHILOSOPHY. 


just  hidden  by  the  edge.  Pour  water  into  the  basin,  the  coin  will 
come  into  sight.  The  rays  which  strike  the  surface  of  the  water  as 
ab  (Fig.  171)  are  refracted  in  the  direction  be,  and  enter  the  eye. 

Experiment  95. — Place  a  stick  obliquely  in  clear  water,  it  appears 
bent :  explain  this. 

279.  Angles  of  Incidence  and  Refraction,— If  the  ray  is 
passing  from  air  into  water,  the  angle  aid  (Fig.  174)  is  called 
the  angle  of  incidence,  and  eld  the  angle  of  refraction. 

280.  Law  of  Sines. — There  is  a  law  of  refraction  called  the  "  law 
of  sines."     This  may  be  explained  by  Fig.  174.     If  a  circle  be  de- 


FIG.  173.— STICK  BENT  BY  REFRACTION. 


FIG.  174. — LAW  OF  SINES. 


scribed  about  the  point  where  the  ray  strikes  the  surface,  and  froni 
the  points  a  and  c,  where  the  incident  ray  and  the  refracted  ray  cut 
this  circle,  perpendiculars  ab  and  cd  be  drawn  to  the  vertical  bd,  then 
the  u  law  of  sines"  is  that  ab  has  to  cd  a  constant 
ratio,  whatever  be  the  angle  of  incidence.  That 
is,  if  ab  is  1%  times  cd,  any  other  line,  ef,  will  also 
be  1 J  times  gh.1 

281.  Limiting1  Angle. — In  passing  into  a 
rarer  medium,  the  angle  of  refraction,  fbd, 
FIG.  175.— LIMITING  is  greater  than  the  angle  of  incidence,  abc. 
For  a  certain  angle  of  incidence,  as  ebc,  the 
angle  of  refraction  becomes  90°,  or  fbg.     This  angle,  ebc,  is 

1  ab  is  said  to  be  a  sine  of  the  angle  of  incidence,  and  cd  of  the 
angle  of  refraction.  This  is  an  expression  used  in  Trigonometry ; 
hence  the  name  of  the  law. 


LIGHT. 


179 


called  the  limiting  angle.    In  the  case  of  air  and  water  it  is 


FIG.  176.— TOTAL  REFLECTION. 

about  48J°.     If  the  angle  of  incidence  is  greater  than  this, 

as  hbc,  the  ray  will  not  leave 
the  water,  but  will  be  re- 
flected from  its  surface,  and 
pass  in  the  direction  bk. 

Experiment  96. — Hold  a  glass 
of  water,  with  spoon,  as  in  Fig. 
177,  so  that  we  may  look  ob- 
liquely at  the  surface  of  the  water 
from  underneath.  There  will  be 
total  reflection  of  the  part  of  the 
spoon  under  water. 

282.  Total  Reflection.— 
This  is  called  total  reflection 
because  all  the  light  is  re- 
flected. This  is  not  the  case 
with  ordinary  reflection. 

If  a  glass  prism  shaped 


FIG.  177.— TOTAL  REFLECTION. 


FIG.  178.— TOTAL  REFLECTION. 


180 


NATURAL  PHILOSOPHT. 


like  abc  be  so  placed  that  the  light  will  fall  vertically  on 
the  face  ab,  it  will  pass  into  the  glass.  It  cannot  pass 
through  the  surface,  ac,  into  the  air,  for  the  angle  of  in- 
cidence, is  greater  than  the  limiting  angle.  The  light 
will  suffer  total  reflection,  and  will  pass  off  in  a  perpen- 
dicular, /,  to  its  former  course. 

283.  Refraction  through  Glass. — If  light  passes  through 

a  piece  of  glass  with 
parallel  sides,  it  is 
refracted  by  both 
surfaces  in  differ- 
ent directions,  and 
emerges  parallel  to 
its  original  course. 
284.  Refraction 
through  a  Prism. — 

If  the  sides  are  not  parallel,  the  light  emerges  in  a  new 
direction. 


FIG.  179.— REFRAC- 
TION BY  GLASS 
WITH  PARALLEL 
SIDES. 


FIG.  180.— REFRACTION  BY 
PRISM. 


Experiment  97. — Procure  a  thick  piece  of  clear  glass  and  hold  it 
so  that  part  of  an  object  shall  be  seen  obliquely  through  it  and  part 
past  the  edge.  The  two  parts  will  not  fit  together. 


FIG.  181. — REFRACTION  BY  PLATE-GLASS. 


Experiment  98. — Procure  a  glass  prism,  and  notice  the  apparent 
change  of  position  of  objects  seen  through  it.  (The  colors  seen  will 
be  explained  farther  on.) 

285.  Explanation  of  Refraction.— The  effects  of  refraction  have 


LIGHT. 


181 


been  illustrated  in  the  following  way.    Suppose  a  combination  of  two 
wheels  and  an  axle  to  be  moved  over  the  floor.     It  will,  if  the  floor  is 


FIG.  182.— REFRACTION  BY  TRIANGULAR  PRISM. 

smooth,  roll  in  a  straight  line.     But  if  it  comes  obliquely  against  a 
square  piece  of  velvet,  the  wheel  that  strikes  first  will  be  delayed,  and 


FIG.  183. — EXPLANATION  OF  REFRACTION. 


FIG.  184.— REFRACTION  BY  CONVEX  LENS. 


the  path  will  be  bent  towards  the  perpendicular  to  the  surface.  When 
it  gets  to  the  other  side,  the  same  wheel  will  reach  the  smooth  floor 
first  and  be  accelerated,  and  so  the  path  will  be  parallel  to  its  origi- 
nal direction. 

16 


182 


NATURAL   PHILOSOPHY. 


If  the  piece  of  velvet  is  convex,  the  effect  will  be  to  bend  the  path 
in  the  same  direction  at  each  surface ;  if  triangular,  as  a  prism  does. 

286.  Lenses. — A  lens  is  a  circular  piece  of  glass  to  refract 
the  rays  of  light.     At  least  one  of  its  surfaces  must  be 


FIG.  185.— LENSES. 


curved.  It  may  be  of  any  of  the  following  shapes:  a, 
double-convex ;  b,  plano-convex ;  c,  concavo-convex ;  d, 
double-concave ;  e,  plano-concave ;  /,  convexo-concave. 


FIG  186. — CONVEX  LENS. 


287.  Effect  of  a  Convex  Lens. — The  effect  of  a  convex  lens 
is  to  cause  rays  of  light  to  converge. 


LIGHT. 


183 


Fia.  187. — EFFECT  OP  A  CONVEX  LENS. 


288.  Effect  of  a  Concave  Lens. — The  effect  of  a  concave 
lens  is  to  cause  rays  of  light  to  diverge. 


FIG.  188. — EFFECT  OF  A  CONCAVE  LENS. 

Experiment  99. — Verify  the  first  of  these  statements  by  means  of 
glasses  from  spectacles,  or  "  magnifying-glasses."  Light  is  concen- 
trated to  a  point. 

To  illustrate  the  properties  of  lenses  we  will  study  the  cases  of 
double-convex  and  double-concave  lenses  of  the  same  curvature  on 
both  sides.  This,  with  a  knowledge  of  the  principles  of  refraction, 
will  enable  anv  one  to  understand  the  effects  of  other  lenses. 


FIG.  189.— PRINCIPAL  Focus. 

289.  Double-Convex  Lens. — A   double-convex    lens  will 


184 


NATURAL  PHILOSOPHY. 


bring  parallel  rays  to  a  point  called  the  principal  focus.  The 
distance  from  the  centre  of  the  lens,  A,  to  the  principal 
focus,  F,  is  called  the  focal  length  of  a  lens. 


FIG.  190. — CONJUGATE  Foci. 


If  the  rays  diverge  from  a  point,  as  A,  they  will  con- 
verge to  another  point,  as  B,  farther  from  the  lens  than  the 


FIG.  191.— CONJUGATE  Foci. 


principal  focus.  If  they  diverge  from  B,  they  will  converge 
at  A.  The  line  joining  A  and  B  will  always  pass  through 
the  centre,  D,  of  the  lens. 


FIG.  192. — MAGNIFYING  EFFECT  OF  A  CONVEX  LENS. 

A  and  B  are  called  conjugate  foci.     If  the  eye  be  placed 
at  F,  the  converging  of  the  rays  from  any  object  beyond 


LIGHT. 


185 


the  lens,  as  AB,  will  cause  an  enlarged  image  of  the  object, 
as  A'  B'.  The  rays  from  A  appear  to  come  from  A',  and  the 
rays  from  B  appear  to  come  from  B',  and  so  for  interme- 
diate points. 

The  eye  and  the  object  must  be  in  the  conjugate  foci  of 
the  lens  for  distinct  vision. 


FIG.  194.-  IMAGE  BY  CONVEX  LENS. 

Experiment  100. — Hold  a  magnifying-glass  so  as  to  see  an  object 
distinctly.  Now  move  the  object  from  the  lens.  The  eye  must  be 
placed  closer  to  the  lens  to  secure  distinct  vision.  As  one  focus  recedes 
from  the  lens,  the  other  approaches. 

Experiment  101. — Hold  a  lens  in  front  of  a  wall  or  a  piece  of  paper 

16* 


186 


NATURAL  PHILOSOPHY. 


so  that  the  light  of  a  candle  will  shine  through  the  lens.  By  moving 
the  lens  to  and  from  the  wall,  the  position  is  found  where  an  image 
of  the  candle  will  be  cast  on  the  wall  or  paper,  inverted. 

Experiment  102. — Try  the  same  in  the  daytime  in  such  a  way  as  to 
throw  an  image  of  the  window  on  the  wall. 

Experiment  103. — When  a  distinct  image  of  a  distant  window  or 
candle  is  thrown  on  the  wall,  measure  the  distance  of  the  lens  from 
the  wall.  This  will  give  approximately  its  focal  length  ;  for  the  rays 
are  nearly  parallel. 

Experiment  104. — Hold  the  lens  in  the  direct  rays  of  the  sun;  ad- 
just it  so  as  to  make  the  circle  of  light  on  the  screen  the  least  possi- 
ble. Measure  again  from  the  screen  to  the  lens.  This  should  agree 
with  the  last  measure.  The  circle  of  light  is  the  image  of  the  sun. 

Fig.  195  shows  why  the  object  is  inverted.  All  rays  from 
a  are  brought  to  a  focus  in  a  line  through  o  at  #',  from  b  at 

&',  from  c  at  cf,  etc.    When 
the   object   is   nearer 
lens   than   the  image 


FIG.  195.— IMAGE  BY  CONVEX  LENS. 


the 
the 

image    will    be    enlarged, 
and  vice  versa. 

Experiment  105.  —In  the  ar- 
rangement of  Fig.  195  move 
the  candle  nearer  the  lens  ;  the 
image  will  recede  and  get  larger. 
Experiment      106. — Having 
found  the  focal  length  by  exper- 
iment 104  or  105,  place  a  candle  at  just  twice  the  focal  length  from 
the  lens  ;  the  image  will  be  the  same  size  as  the  object. 

Experiment  107. — Place  the  candle  at  the  principal  focus.     There 
will  be  no  image,  for  all  the  rays  move  out  parallel. 

Experiment  108. — Place  the  image  still  nearer  the  lens.     The  rays 
will  diverge,  and  will  form  no  real  image. 

290.  Construction  of  the  Image.— The  position  and  size 

of  the  real  image  can  be  con- 
structed in  the  various  cases 
as  follows. 

Draw  the  parallel  ray  ad. 
It  will  be  refracted  through 
the  principal  focus  /.  Also 
draw  the  line  ao  through  the 
centre.  Where  these  meet  will  be  the  position  of  the  image 
of  the  point  a.  The  same  may  be  done  from  other  points. 

291.  Concave  Lens. — Since  a  bundle  of  rays  from  a  point 


FIG.  196.— CONSTRUCTION  OF  THE  IMAGE. 


LIGHT. 


187 


are  made  to  diverge  still  more  by  concave  lenses,  they  do 
not  form  real  images.  The  images  are  smaller  than  the 
objects,  and  are  erect. 

The  principal  focus  is  the  point  from  which  parallel  rays 
appear  to  diverge. 

292.  Spherical  Aberration. — A  spherical  convex  lens  will 
not  bring  all  rays  to  exactly  the  same  point.     The  rays 
near  the  edge   are    refracted   more  than  those  near  the 
centre.      Thus,   while  rays  like  db 

are  brought  to  a  focus  at  c,  those 
like  ed  are  refracted  to  g,  and  hence 
a  perfectly  distinct  image  is  -not 
formed.  This  is  called  "spheri- 
cal aberration,"  and  has  to  be  cor- 
rected for  by  deviations  in  the  lenses 
from  the  spherical  form. 

293.  Atmospheric  Refraction, — When  a  ray  of  light  en- 
ters the  atmosphere  from  the  sun  or  a  star,  it  is  refracted  j 
as  it  enters  each  denser  layer,  it  is  more  and  more  refracted, 
being  always  bent  towards  the  perpendicular  to  the  sur- 
face, so  that  it  finally  enters  the  eye  as  if  it  came  from  a 
point  higher  up  in  the  sky  than  it  really  does.    The  effects 
of  this  are  principally  important  to  astronomers. 

294.  Mirage. — In  hot  and  sandy  deserts  the  surface  layers 


Fia.   197.  —  SPHERICAL  ABERRA- 
TION. 


FIG.  198.— MIRAGE. 


of  air  are  sometimes  so  expanded  by  the  heat  as  to  be  rarer 
than  those  above.   Rays  from  a  distant  object  are  then  bent 


188 


NATURAL   PHILOSOPHY. 


in  the  other  direction,  until  finally,  reaching  the  lowest 
angle,  they  suffer  total  reflection.  These  strata  from  which 
the  objects  and  sky  are  reflected  appear  as  a  glassy  pool. 
The  illusion  is  called  mirage. 


IV.— DISPERSION. 


295.  Dispersion. — When  light  passes  from  one  medium 
into  another  of  different  density,  the  light  is  not  only  re- 


FIG.  199.— DISPERSION  OF  LIGHT. 

fracted,  but  the  image  of  the  object  is  seen  to  be  surrounded 
by  a  fringe  of  color. 

Experiment  109. — Look  through  a  prism  of  glass,  and  notice  the 
colored  fringes  surrounding  objects.  Allow  the  direct  rays  of  the  sun 
to  shine  through  the  prism,  and  notice  the  rainbow-colors  thrown  on 
the  wall  or  on  any  object  in  the  room. 


LIGHT.  189 


Instead  of  a  glass  prism  it  is  much  better  to  use  a  triangular  bottle 
filled  with  carbon  bisulphide. 

Experiment  no. — With  such  a  prism,  allow  a  beam  of  light  to 
pass  into  a  room  through  a  narrow  slit.  Or  obtain  a  beam  from  a 
projecting  lantern,  and  pass  it  through  the  slit.  Place  in  front  of  the 
slit  a  prism  of  glass,  which  may  often  be  obtained  from  off  a  lamp. 
Or,  better,  directly  in  front  of  the  slit  place  a 
double-convex  lens  in  such  a  position  as  to 
throw  a  well-defined  image  of  the  slit  on  a 
wall  or  a  screen.  In  the  path  of  the  light,  after 
passing  through  the  lens,  set  a  carbon  bisul- 
phide  prism.  A  beautiful  band  of  colors  will  *««r 
now  be  seen  on  the  wall,  not,  however,  di- 
rectly in  front  of  the  slit. 

296.  Spectrum.-This  band  of  colors     FIQ  200._DISPERSION. 
is  called  a  spectrum,  and  the  separation 

of  the  beam  of  light  into  tbe  various  colors  is  called  dis- 
persion. 

297.  Order  of  Colors. — By  an  examination  of  the  spectrum 
it  will  be  seen  that  the  colors  are  arranged  in  this  order, — 
violet,  indigo,  blue,  green,  yellow,  orange,  and  red ;  that 
the  violet  is  refracted  from  its  straight  course  the  most,  and 
the  red  the  least. 

298.  Cause  of  Spectrum. — We  may  now  see  the  cause 
of  the  spectrum.     All  these  colors  existed  in  the  beam  of 
light  as  it  came  through  the  slit.     But  the  prism  refracted 
them  differently,  turning  the  violet  aside  the  farthest,  tben 
the  indigo,  and  so  on,  and  projecting  them  at  different 
places  on  the  screen.     If  they  are  all  united,  the  original 
white  light  will  be  produced. 

Experiment  in. — Hold  a  mirror  in  front  of  the  prism  so  as  to 
throw  the  spectrum  on  the  ceiling.  Kapidly  rotate  the  mirror,  so  that 
the  colors  shall  blend  together  on  the  ceiling.  The  image  will  now  be 
white. 

299.  Color-Disk. — A  color-disk  is  a  circular  piece  of  paste- 
board, on  which  are  pasted  sectors  of  colored  paper  contain- 
ing the  rainbow-colors.    When  this  is  rapidly  revolved,  the 
colors  all  blend  together  in  the  eye  and  make  white  or  gray. 

If  the  colors  were  perfectly  pure  and  well  lighted  up, 


190 


NATURAL   PHILOSOPHY. 


the  disk  would  be  entirely  white.     The  gray  tint  is  pro- 
duced by  the  impurity  of  the  colors. 


FIG.  201.— COLOR-DISK. 

300.  Waves  of  Different  Lengths.— It  has  been  said  that 
light  is  propagated  in  waves.     All  waves  of  light  are  not, 
however,  of  the  same  length,  nor  do  all  have  the  same  quick- 
ness of  vibration.     Experiment  has  shown  that  the  vibra- 
tions of  the  violet  rays  are  shorter  and  more  rapid  than 
those  of  other  colors,  the  indigo  next,  and  then  in  the  order 
of  arrangement  in  the  spectrum.     When  light  made  up  of 
all  these  waves  strikes  the  prism,  the  short,  quick  vibrations 
of  violet  are  turned  aside  the  most,  and  the  larger  and 
slower  vibrations  of  red  the  least.     This  is  the  cause  of 
dispersion. 

Experiment  112. — Stand  with  the  eye  in  the  spectrum  looking 
towards  the  prism.  The  different  colors  will  be  seen  in  order  as  the 
eye  changes  from  side  to  side. 

301.  The  Spectroscope. — This  explains  the  spectroscope. 
In  the  end  of  the  right-hand  telescope  is  a  narrow  slit, 


LIGHT. 


191 


through  which  the  light  enters.     The  eye  looks  towards 
the  prism  through  another  telescope,  which  magnifies  ob- 


IlIlKalllli 

FIG.  202. — THE  SPECTROSCOPE. 

jects,  and  sees  the  spectrum  directly.  The  third  telescope 
is  for  the  purpose  of  throwing  a  scale  into  view,  so  as  to 
determine  the  positions  of  the  various  colors. 

When  used  for  celestial  objects,  this  is  attached  to  the 
eye-end  of  a  telescope,  so  that  the  light  from  the  object  after 
going  through  the  telescope  will  pass  into  the  slit. 

302.  Effect  of  a  Train  of  Prisms. — If  the  light,  after  pass- 
ing through  one  prism,  falls  on  another,  the  spectrum  will 
be  further  dispersed.     By  using  more  prisms  the  spectrum 
may  be  made  of  any  required  length,  though  each  disper- 
sion causes  a  loss  of  some  light,  due  to  reflection  from  the 
faces  of  the  prism. 

303.  Different  Spectra  from  Solids  and  Gases. — Light 
coming  from  glowing  lime,  or  from   the   heated  carbon 
particles  in  the  flame  of  a  lamp  or  candle,  will  give  similar 


192  NATURAL   PHILOSOPHY. 

spectra,  differing  only  in  brightness.  If,  however,  the 
spectrum  of  glowing  vapor  of  sodium,  made  by  sprinkling 
a  little  common  salt  in  an  alcohol,  or  Bunsen  burner,  flame, 
be  examined  with  a  spectroscope,  it  will  be  seen  to  consist 
of  one  or  two1  yellow  bands  only.  There  will  be  no  red, 
green,  or  any  of  the  other  colors.  If  a  vapor  of  strontium 
be  formed  in  the  same  way,  there  will  be  bands  or  lines  of 
red,  yellow,  and  blue,  and  not  of  the  others.  In  this  way 
every  substance  has  its  own  peculiar  lines  when  reduced  to 
the  state  of  a  glowing  gas  and  examined  with  a  spectro- 
scope. We  may  thus  judge  of  the  composition  of  a  sub- 
stance by  the  character  of  its  spectrum,  Glowing  solids  and 
liquids  give  continuous  spectra,  the  colors  running  into  one  an- 
other, and  all  are  alike.  But  gases  give  spectra  of  bright  lines, 
and  each  gas  has  its  peculiar  spectrum.  Several  are  shown  in 
the  frontispiece. 

304.  Dark-Line  Spectra. — If  the  light  passes  from  a  glow- 
ing solid  through  a  gas,  the  spectrum  shows  all  the  colors ; 
but  it  is  crossed  by  dark  lines,  and  the  most  careful  measure- 
ments, as  well  as  theory,  show  that  these  lines  are  in  the 
exact  position  of  the  bright  lines   which  the  gas  gives  out 
by  itself.     Thus,  if  the  light  passes  through  sodium  vapor 
there  are  seen  in  the  yellow  of  the  spectrum  two  dark  lines 
side  by  side.     If  in  examining  a  heavenly  body  we  found 
such  a  spectrum  as  this,  it  would  therefore  indicate  the 
composition  of  the  vapor  through  which  the  light  passed, 
but  not  the  composition  of  the  substance  giving  the  light ; 
the  position  of  the  dark  lines  would  tell  of  the  vapor  which 
made  them,  while  the  continuous  spectrum  would  not  tell 
the  character  of  the  substance  giving  the  light,  except  that 
it  was  not  a  gas  under  ordinary  pressure. 

305.  Solar  Spectrum. — The  solar  spectrum  is  seen  in  the 
frontispiece.     We  infer  from  this  that  the  sun  is  a  glowing 

1  There  are  two,  but  so  close  together  that  often  they  are  not  sepa- 
rated. 


LIGHT.  193 


solid  or  liquid  substance,  and  has  an  atmosphere  of  gas, 
which  produces  the  dark  lines. 

306.  Cause  of  the  Dark  Lines. — The  cause  of  these  dark 
lines  is  as  follows.    A  gas  has  power  to  take  from  light  the  same 
vibrations  which  it  gives  out  when  glowing.     When  light  from 
glowing  lime  shines  through  sodium  vapor,  the  vapor  ab- 
stracts from  the  light  the  particular  vibrations  that  make 
up  yellow  light.     The  dark   lines  therefore   indicate  the 
absence  of  the  spectrum  in  those  positions.     It  is  true  that 
the  vapor  gives  its  own  bright  yellow  lines,  but  they  are 
faint  compared  with  the  spectrum  from  the  solid,  and  hence 
look  dark  by  comparison. 

307.  Convergence  of  Spectra. — As  a  glowing  gas  becomes 
cooled  down,  the  bright  lines  which  it  shows  in  the  spec- 
trum broaden  into  bands,  till  finally,  when  it  cools  down  to 
the  state  of  a  glowing  liquid  or  solid,  the  bands  run  together, 
and  a  continuous  spectrum  is  formed.    This  shows  that  the 
two  kinds  of  spectra  are  not  so  distinct  as  would  at  first 
be  supposed. 

308.  Heat-Rays. — The  rays  which  convey  the  impression 
of  heat  from  a  glowing  solid  are  also  refracted  and  dis- 
persed by  a  prism.     They  are  the  same  rays  as  the  light- 
rays,  and  extend  also  on  both  sides  of  the  visible  spectrum, 
more  especially  on  the  red  side.    The  rays  by  which  photo- 
graphing is  done  lie  principally  about  the  violet  end  of  the 
spectrum. 

309.  The  Sun  Blue. — Prof.  Langley  has  recently  shown 
that  the  atmosphere  quenches  much  more  of  the  rays  near 
the  violet  end  than  of  those  near  the  red  end  of  the  spec- 
trum, and  that  if  we  could  see  the  sun  outside  our  atmos- 
phere it  would  appear  blue  rather  than  yellow,  as  it  does. 

310.  The  Rainbow. — The  rainbow  is  a  spectrum.     Kain- 
drops  are  the  prisms.     Whenever  a  ray  of  light  enters  one 
of  these  drops  there  is  refraction,  and  wherever  there  is 
refraction  there  is  dispersion. 

The  red  is  on  the  outside  of  the  arc,  and  the  violet  on 
i        n  17 


194 


NATURAL  PHILOSOPHY. 


the  inside.  When  there  is  a  fainter  secondary  bow  the 
order  of  colors  is  reversed.  The  radius  of  the  arc  is  about 
410,1  and  its  centre  is  always  exactly  opposite  the  sun. 

"When  the  sun  is  just  setting,  how  much  of  a  circle  is  seen  ?  how 
near  to  the  horizon  must  the  sun  be  to  make  a  bow  ? 

The  path  of  the  rays  through  a  drop  is  seen  in  Fig.  203. 
From  S  the  rays  come,  are  refracted  at  I,  reflected  at  A,  and 


FIG.  203. — PATH  OF  RAYS  TO  FORM  PRIMARY  Bow. 

again  refracted  at  I',  and  pass  out  dispersed  towards  M.  The 

lines  SI  and  I'M  make 
an  angle  of  about 
41°  with  each  other. 
Hence  a  person 
standing  so  that  he 
would  receive  these 
rays.  I'M,  would  have 
them  colored.  But 
the  air  is  full  of  drops. 
Those  in  such  a  posi- 

FIG.204.-PATH  OF  BAYS  TO  FORM  SECONDARY  Bow.        ^     ^     anyinstant 

as  to  send  the  ray  to  the  observer  would  always  be  41°  (for 


1  A  little  less  than  half  the  distance  from  the  horizon  to  the  zenith. 


LIGHT.  195 


the  red  42£°,  and  for  the  violet  40  J°)  distant  from  the  point 
opposite  the  sun,  and  hence  would  lie  in  an  arc  of  a  circle. 

Other  rays  which  enter  the  drop  are  also  refracted,  but 
only  those  which  pass  as  in  the  figure  are  kept  together  so 
as  to  make  an  impression.  The  remainder  are  scattered. 

The  secondary  bow  is  produced  by  two  refractions  and 
two  reflections,  as  in  Fig.  204. 

Fig.  205  shows  the  formation  of  both  bows,  a  and  a' 
indicate  the  position  of  the  drops  which  form  the  violet 
rays,  and  b  and  b'  that  of  the  drops  which  form  the  red  rays. 


>  Z 

FIG.  205.— FORMATION  OF  PRIMARY  AND  SECONDARY  Bows. 

311.  Halos. — Halos  are  circles  of  light  around  the  sun 
or  moon,  formed  by  refraction  from  crystals  of  ice  floating 
in  the  air.  They  are  seen  in  summer  as  well  as  in  winter, 
for  the  cold  of  the  upper  regions  makes  ice-crystals  at 
any  time  of  the  year.  When  formed  by  the  sun,  there  is 
often  sufficient  light  to  show  the  colors  of  the  rainbow. 


196 


NATURAL   PHILOSOPHY. 


A  section  of  an  ice-crystal  is  often  of  the  shape  of  a  six- 
sided  figure.  When  rays  enter  one  face  they  are  sometimes 
refracted  so  that  they  emerge  from  the  next  face  but  one. 
This  forms  the  smallest  and  most  common  halo,  with  a 
radius  of  about  22°.  Sometimes  the  rays  enter  a  side  and 
come  out  at  the  base.  This  makes  a  larger  and  fainter 
halo. 


FIG.  206.— HALOS  AND  PARHELIA. 

312.  Parhelia. — There  is  often  also  a  circle  of  white  light 
parallel  to  the  horizon,  formed  by  reflection  from  crystals  of 
ice  suspended  vertically  in  the  atmosphere.  This  cuts  the 
halos  in  two  points.  In  these  points  the  light  is  concen- 
trated, some  coming  from  the  halo  and  some  from  the  circle 
of  reflection,  and  parhelia  (otherwise  called  "  mock  suns,"  or 
"  sun-dogs")  are  formed. 


LIGHT. 


197 


In  Fig.  206,  the  bright  spots  are  parhelia.     The  various 
curves  are  produced  by  varied  refractions  and  reflections. 

Fig.  207  shows  circles  seen  in  the  United  States  in  Janu- 
ary, 1883.  In  this 
case  parhelia  were 
noticed  at  C,  D, 
C',  and  D',  even 
though  no  halos 
were  seen  from  C 
and  C'  and  D  and 
D'.  Distinct  ones 
were  noticed  at 
A,  B,  A',  and  B', 
and  two  colored 
halos. 

313.  Colors   of 

Opaque  Objects. —  "  ^  -  - -  -  ^  "' 

It   has    been    Said        Fia  207.— HALOS  AND  PARHELIA  OF  JANUARY,  1883. 

that      the     light 

which  opaque  objects  diffuse  is  that  by  which  they  are  seen. 
But  the  light  which  they  diffuse  after  it  has  entered  slightly 
within  their  surfaces  is  generally  different  from  that  which 
falls  upon  them.  Their  surfaces  have  the  power  of  choosing 
out  certain  rays  from  the  white  light  which  is  incident  to 
them,  and  of  destroying  them.  The  remainder  is  diffused, 
and  gives  the  objects  their  colors.  If  the  colors  of  the  red 
end  of  the  spectrum  are  absorbed,  the  object  will  appear  of 
some  shade  of  blue.  If  the  red  and  blue  are  both  absorbed, 
the  remaining  colors  will  mix,  and  the  general  effect  will 
be  green.  If  nothing  is  absorbed,  the  color  is  white ;  and 
if  all  is  absorbed,  the  object  will  appear  black. 

314.  Colors  of  Transparent  Objects. — If  the  object  is  trans- 
parent, it  may  be  seen  by  the  color  which  it  transmits. 
Blue  glass  transmits  the  blue  rays,  and  quenches  or  reflects 
the  rest.   Sometimes  a  piece  of  glass  is  seen  to  be  of  one  color 
by  transmitted  light  and  of  another  color  by  diffused  light. 

17* 


198  NATURAL  PHILOSOPHY. 

Experiment  113. — Place  a  piece  of  blue  glass  in  the  path  of  the 
light  which  passes  through  the  prism.  The  red  end  of  the  spectrum 
will  be  quenched,  the  blue  end  will  be  undisturbed.  Try  the  same 
with  glass  of  different  colors. 

315.  Cause  of  Blue  Sky. — The  little  particles  of  aqueous 
vapor  and  other  things  which  exist  in  the  air  are  so  minute 
as  to  reflect  only  the  short  blue  vibrations.     Hence  the  sky 
appears  blue  by  reflected  light.   When  near  sunset,  the  sun 
is  shining  through  a  great  stretch   of  air.1     The  blue  is 
largely  taken  out  of  his  rays  by  this  process  of  reflection, 
and  the  red  is  transmitted  to  the  eye.    The  blue  rays  make 
the  blue  sky  of  places  west  of  us.     The  clouds  being  lit  up 
by  this  red  light  which  remains,  seem  to  be  of  a  ruddy 
color.     If  there  are  no  clouds,  the  strata  of  air  nearest  the 
horizon  are  of  a  reddish  hue,  which  hue  imperceptibly  shades 
into  the  blue  of  the  zenith  through  the  intermediate  shades 
of  the  spectrum, — orange,  yellow,  green, — more  and  more 
of  reflected  blue  light  being  mingled  with  the  transmitted 
red  as  we  recede  from  the  horizon. 

316.  Primary  Colors. — All  the  colors  seen  on  the  earth 
are  composed  of  one  of  the  colors  of  the  spectrum  or  of 
several  of  them  blended  together.     Furthermore,  all  the 
colors  of  the  spectrum  are  composed  of  one  or  more  of 
the  three  primary  colors, — red,  green,  and  violet.     Eed  and 
green  mixed  in  varying  proportions  produce  the   colors 
which  lie  between  them,  and  green   and  violet  the  rest. 
Red  and  violet  produce  shades  of  purple.     Therefore,  also, 
red,  green,  and  violet  produce  white. 

Experiment  114. — Collect  together  a  number  of  objects  of  different 
colors  in  a  dark  room,  and  light  them  up  by  the  light  of  a  sodium 
taper,  made  by  holding  metallic  sodium  or  common  salt2  in  the  flame 
of  a  Bunsen  burner  or  an  alcohol  lamp.  If  the  flame  is  bright  enough, 
the  effect  is  very  striking.  Yellow  colors  are  brought  out  plainly. 
All  others  appear  dark  or  of  some  shade  of  gray. 

317.  Only  Yellow  in  Sodium  Flame. — It  has  been  shown 

1  Show  this  by  a  diagram. 

8  A  pine  stick  soaked  in  a  solution  of  salt  will  answer  well. 


LIGHT.  199 


that  when  the  sodium  flame  is  analyzed  by  a  spectroscope 
nothing  is  found  in  it  but  yellow  light.  Hence,  when  it 
falls  on  objects,  only  those  which  can  diffuse  yellow  light 
are  colored.  The  others  quench  it  and  appear  dark.  An 
object  cannot  appear  red  or  green,  because  no  light  con- 
taining these  colors  falls  on  it. 

Experiment  115. — Place  a  strip  of  red  paper  in  the  red  part  of  the 
spectrum.  It  will  appear  of  its  natural  color.  Place  it  in  the  blue.  It 
will  appear  black.  Ked  paper  quenches  blue  rays  and  diffuses  red.  Try 
the  same  with  paper  of  other  colors.  Most  colored  objects  are  colored 
by  a  mixture  of  the  spectrum  colors  :  hence  they  may  reflect  more 
than  one. 

318.  Complementary  Colors. — We   have  said  that  red, 
green,  and   violet   produce  white.      Hence  a  mixture  of 
green  and  violet,  as  bluish  green,  will  produce  white  when 
combined  with  red.     Also,  since  purple  is  a  combination  of 
red  and  violet,  purple  and  green  colors  will  produce  white. 
Two  colors  which,  when  mixed  together,  produce  white  are 
called  complementary  colors.     The  mixture  of  any  two  of 
the  primary  colors  is  complementary  to  the  third.     We 
can  obtain  complementary  colors  by  combining  violet  with 
bluish  green  for  one  shade,  and  red  with  yellowish  green 
for  the  other.     The  whole  spectrum  must  be  included  in  the 
two  colors.     The  names  of  some  of  the  prominent  comple- 
mentary colors  are  as  follows : 

Red  and  bluish  green. 
Orange  and  turquoise-blue. 
Yellow  and  ultramarine. 
Yellowish  green  and  violet. 
Green  and  purple. 

Two  colors  which  are  complementary  show  in  contrast 
to  better  advantage  than  two  others. 

319.  Blue  and  Yellow. — If  solutions   of  aniline-yellow 
and  ammoniacal  sulphate  of  copper  be  placed  in  tanks  with 
parallel  sides,  and  light  be  passed  through  them  so  as  to 
be  thrown  on  the  screen  in  the  same  place,  the  mixture  of 
the  blue  and  yellow  colors  will  produce  white. 


200  NATURAL  PHILOSOPHY. 


Experiment  116. — Make  two  solutions  of  blue  and  yellow  liquids, 
and  pour  them  together ;  the  resulting  liquid  will  be  green. 

The  green  is  produced  because  the  blue  liquid  allowed 
the  colors  from  green  to  violet  to  pass,  and  the  yellow 
those  from  green  to  red.  Green  is  the  only  color  which 
both  allow  to  pass,  hence  the  mixture  as  seen  by  trans- 
mitted light  is  green. 

320.  Effects  of  Complementary  Colors. — After  the  eye  has 
seen  one  color  for  a  time,  it  gives  to  other  objects  the  com- 
plementary color. 

Experiment  117. — Make  a  broad  black  ink-mark  on  green  paper, 
and  cover  it  with  white  tissue-paper.  The  mark  will  appear  red. 

This  is  an  optical  illusion.  The  eye  is  filled  with  green 
rays,  and  the  tendency  is  to  see  other  objects  of  the  comple- 
mentary color.  The  white  tissue-paper  tones  down  the 
intense  blackness  of  the  mark,  which  would  otherwise,  by 
its  distinctness,  prevent  the  illusion. 

321.  Interference   Of   Rays. — Color  is  sometimes  produced  by 
interference  of  waves  of  light.     This  means  that  two  waves  so  meet 
each  other  that  the  depression  of  one  corresponds  to  the  elevation  of 
the  other,  so  that  they  neutralize  each  other,  as  we  have  seen  in  the 
case  of  water-waves  (page  87).     If  in  white  light  the  colors  of  the  red 
end  of  the  spectrum  are  thus  neutralized,  the  resulting  effect  is  blue. 
If  the  blue  and  the  red  are  neutralized,  the  color  may  be  green. 

322.  Colors    of    Soap-Bubbles.— This   effect   is   seen   in   soap- 
bubbles. 

Experiment  118. — Make  a  liquid  out  of  good  Castile  soap  and  a 
little  glycerine  and  water,  and  blow  some  soap-bubbles.  Notice  how 
beautifully  the  colors  chase  one  another  over  the  film. 

The  light  is  reflected  to  us  from  the  outer  and  also  from  the  inner 
surface  of  the  film.  If  the  thickness  of  the  film  is  just  a  quarter 
of  a  wave-length,  the  light  that  comes  from  the  inner  surface,  having 
to  pass  twice  through  the  film,  is  just  one-half  a  wave-length  behind 
that  which  is  reflected  by  the  outer.  If  the  film  were  three-quarters  of 
a  wave-length  thick,  it  would  be  one  and  a  half  wave-lengths  behind; 
and  so  on.  In  all  these  cases  there  would  be  destruction  of  light- 
waves. As  the  film  is  continually  changing  its  thickness,  and  as  the 


LIGHT.  201 


wave-lengths  of  the  different  colors  vary,  there   is  a  continually 
changing  view  of  colors  seen  on  the  bubble. 

323.  Diffraction. — Another  effect  of  interference  is  shown  in  what 
is  commonly  called  diffraction.     If  light  passes  through  a  very  nar- 
row opening,  fringes  of  color  are  seen  along  its  sides.     These  are  due 
to  the  fact  that  the  waves  of  light  radiating  in  all  directions  from  the 
opening  come  in  contact,  and  certain  vibrations  destroy  one  another, 
leaving  the  resulting  colors. 

324.  Gratings. — Another  form  of  diffraction  is  produced  by  sub- 
stances  whose  surfaces  are  covered  with  parallel   lines  very  close 
together.     This  is  shown  in  mother-of-pearl  shells,  where  the  edges 
of  the  layers  constitute  the  lines.     This  is  caused  by  interference  of 
the  rays  reflected  from  the'different  surfaces.     Glass  or  any  metallic 
surface  ruled  by  fine  lines  affords  an  excellent  substitute  for  a  prism  in 
a  spectroscope.     The  diffraction  spectra  are  not  so  bright  as  the  pris- 
matic from  the  same  source,  as  not  nearly  all  the  light  is  reflected,  but 
the  colors  are  purer.     The  finer  and  closer  the  lines,  the  better  will 
be  the  spectrum. 

Exercises. — 1.  What  difference  is  there  between  the  causes  of  the 
color  of  a  red  book  and  of  red  glass  ? 

2.  Why  are  some  objects  of  different  colors  by  candle-light  from 
what  they  are  by  daylight? 

3.  If  the  sun  were  composed  of  glowing  sodium  vapors  only,  what 
colors  should  we  have  on  the  earth  ? 

4.  What  difference  in  color  is  there  between  the  electric  light  and 
gas-light,  and  what  would  be  the  effect  of  this  difference  on  the  colors 
of  objects  lit  up  by  them  ? 

5.  Why  will  a  strip  of  red  glass  cast  a  shadow  on  the  blue  of  the 
spectrum  and  not  on  the  red  ? 

6.  Will  there  be  any  difference  in  the  effect  on  the  spectrum  if  a 
piece  of  colored  glass  is  held  in  the  path  of  the  ray  after  and  before 
it  passes  through  the  prism  ? 

7.  If  held  as  in  the  former  case,  which  part  of  the  spectrum  will  be 
seen  on  a  piece  of  red  glass  ? 

8.  A  star  gives  a  spectrum  crossed  by  bright  lines  :  what  is  its 
general  constitution  ? 

9.  Certain  parts  of  a  comet  give  a  spectrum  of  bright  lines  only  : 
what  does  this  indicate  ? 


UNIVERSITY  OF  CALIFQRf 

DEPARTMENT  OF  PHYSICS 


202 


NATURAL  PHILOSOPHY. 


V.— POLARIZATION. 

325.  Polarization. — In  water,  while  the  wave  moves  hori- 

zontally, every  particle  vibrates  vertically. 
In  light  the  motion  is  also  perpendicular  to 
the  direction  of  propagation  of  the  ray,  but 
at  all  angles  to  the  vertical.  Thus,  if  a 
beam  be  supposed  to  move  in  a  direction 
FIG.  208.— TRANSVERSE  perpendicular  to  this  page,  the  vibrations 

SSE* OF  BAY  OF  of  the  ether  are  not  °nly in  tne  line  ab> but 

also  in  all  other  lines,  as  cd,  6/,  etc.  When 
all  the  vibrations  are  quenched  except  such  as  move  in  one 
direction,  as  ab,  the  light  is  said  to  be  polarized. 

326.  Polarization  by  Crystals. — This  can  be  produced  in 

various  ways.  Plates  cut  from 
crystals  of  tourmaline  *  parallel  to 
the  axis  have  the  power  to  de- 
stroy all  vibrations  except  such 
as  are  parallel  to  the  axis,  li  we 
could  suppose  the  crystal  to  be 
made  up  of  bars  which  cut  off 
all  vibrations  across  them,  we 
should  have  the  effect.  Hence 
a  beam  of  light  passing  through 
such  a  plate  is  polarized.  While 
there  is  no  change  in  it  visible 
to  the  eye,  the  polarization  can 
be  detected  by  means  of  another 

similar  plate.  If  this  is  held  so  that  its  axis  is  parallel  to 
that  of  the  first,  so  that  the  "  bars"  of  the  two  run  in  the 
same  direction,  the  light  will  still  pass  through.  If  it  is  held 
at  right  angles,  so  that  one  destroys  the  rays  which  have 
passed  through  the  other,  no  light  will  pass  through.  By 


FIG.  209.— CRYSTAL  OF  TOURMA- 
LINE. 


1  Tourmaline  is  a  semi-transparent  mineral,  crystallizing  in  long 
prisms.     The  axis  runs  parallel  to  its  greatest  length. 


LIGHT. 


203 


gradually  revolving  it  from  this  latter  position,  more  and 
more  light  can  be  seen.  This  is  most  readily  experimented 
with  by  a  pair  of  "  tourmaline  tongs,"  in  one  fork  of  which 


FIG.  210.— TOURMALINE  TONGS. 

the  crystal  can  revolve.  The  first  plate  is  called  the  polar- 
izer, the  second  the  analyzer. 

327.  Polarization  by  Reflection. — Light  can  also  be  po- 
larized by  reflection.     If 

a  ray  be  allowed  to  fall 
on  a  plate  of  glass  at  an 
angle  of  incidence  which 
is  about  57°,  it  will  be 
polarized  in  the  plane  of 
reflection.  That  is,  the 
vibrations  will  now  be  in 
lines  parallel  to  the  re- 
flector, and  others  will 
be  destroyed.  If  the  re- 
flected ray  fall  on  a  second 
plate  at  the  same  angle, 
it  may  be  revolved  so  as 

to  destroy  the  rays  which  the  other  keeps,  or  to  keep  them, 
and  the  polarization  will  be  made  evident.  When  placed  in 
a  position  to  reflect  the  light,  as  in  Fig.  211,  there  will  be 
no  apparent  change  in  brightness,  but  when  the  analyzer 
is  revolved  90°  the  whole  ray  will  be  quenched.  Such  an 
instrument  as  this  is  one  form  of  polariscope. 

328.  Polarization  by  Refraction.— There  is  still  another 


FIG.  211.— POLARISCOPE. 


204 


NATURAL  PHILOSOPHY. 


method  of  polarizing.     If  a  crystal  of  Iceland  spar   be 
placed  over  a  mark,  the  mark  will  appear  double.     The 


Fia.  212. — CBYSTAL  OF  ICELAND  SPAR. 


FIG.  213.— DOUBLE  REFRACTION. 


FIG.  214. 


FIG.  215. 


crystal  has  the  power  not  only  of  separating  the  two  vibra- 
tions, but  of  polarizing  the  parts,  so  that  while  one  ray  is 

polarized  in  one  plane  the  other 
is  in  a  plane  perpendicular  to 
this.  If  the  direction  of  vibra- 
tion of  one  ray  be  in  the  line 
of  Fig.  214,  the  direction  of  the 
other  will  be  shown  in  Fig.  215. 

329.  Colors  by  Polarization. — If  a  plate  of  selenium l  or  a 
piece  of  glass  under  compression  be  placed  between  the  two 
plates  of  tourmaline  of  Fig.  210,  a  beautiful  series  of  col- 
ored rings  will  be  seen.     If  the  analyzer  be  rotated  through 
90°,  the   colors   will   change   to  complementary.      These 
colors  are  due  to  interference. 

330.  Uses  of  the  Polariscope. — The  polariscope  is  used  in 
testing  sugar,  to  determine  the  strength  of  a  solution.    An 
analyzer  is  also  used  to  determine  whether  the  light  from 
comets,  the  solar  atmosphere,  and  other  heavenly  appear- 
ances is  polarized  or  not,  thus  determining  whether  it  is 
light  radiated  directly  by  the  body  or  sunlight  reflected 
from  it. 


1  An  impure  form  of  this  is  gypsum,  or  land-plaster. 


LIGHT. 


205 


VI.— OPTICAL  INSTRUMENTS, 
331.  Microscope. — The  simplest  form  of  microscope  is 


FIG.  216. — SIMPLE  MICROSCOPE. 


a  double-convex  lens,  or  magnifying-glass.  Here  we  see 
an  image  of  an  object  placed 
within  its  focal  length  magni- 
fied, because  the  rays  are  re- 
fracted so  as  to  enter  the  eye  as 
if  they  came  from  a  larger  ob- 
ject. The  more  convex  the  lens, 
the  greater  is  the  magnifying 
power.  When  very  great  power 
is  required,  it  is,  however,  better 
for  clearness  of  view  to  use  two 
or  more  lenses  of  less  curvature. 
The  one  next  the  object  is  the 
object-glass^  or  objective ;  the  one 
next  the  eye  is  the  eye-piece,  or 
ocular. 

The  object-glass  makes  a  real 
and  inverted  image  of  the  object. 
This  image  is  viewed  by  the  eye- 
piece as  if  it  were  an  object.  It 
does  not  reinvert  the  image; 

18 


Fia.  217.— THE  MICROSCOPE. 


206  NATURAL   PHILOSOPHY. 

hence,  with  respect  to  the  original  object,  the  final  image 
is  inverted.  Fig.  217  gives  the  course  of  rays  through  a 
microscope. 

332.  Telescope. — In  a  telescope  the  principle  is  the  same. 


FIG.  218. — PRINCIPLE  OF  THE  REFRACTING  TELESCOPE. 

An  image  of  a  distant  object  is  formed  at  the  focal  length 
of  the  objective,  and  is  magnified  by  the  eye-piece. 

In  the  microscope  the  image  of  the  object  is  greater  than 
the  object,  and  in  the  telescope  it  is  less.  In  the  former 
the  image  increases  as  the  focal  length  of  the  objective  de- 
creases ;  that  is,  as  the  curvature  becomes  greater.  In  the 
latter,  for  distant  objects,  the  image  increases  as  the  focal 
length  increases ;  that  is,  as  the  lens  is  made  flatter. 

333.  Object-Glass. — To  make  a  good  objective,  it  has  to 
be  corrected  not  only  for  spherical  aberration  (page  187), 
but  also  for  the   dispersion  produced  by  the  glass.     This 
would  have  the  effect  of  producing  spectra  and  surround- 
ing all  objects  with  fringes  of  color.    This  is  chromatic  aber- 
ration.    The  method  of  making  the  correction  is  as  follows. 
A  double-convex  lens  of  crown  glass  is  combined  with  a 
plano-concave  lens  of  flint  glass.    These  glasses,  being  differ- 
ently made,  have  different  internal  structure.    The  tendency 
of  the  flint  glass  is  to  neutralize  the  dispersive  effects  of  the 
crown  glass,  but  not  its  refractive  effects,  except  in  part. 
Hence  the  rays  are  brought  to  a  focus,  and  the  colors  are 
not  much  seen ;  though  it  is  impossible  to  make  the  correc- 
tion complete. 

334.  Refracting  and  Reflecting  Telescopes,— Such  tele- 
scopes as  the  above  are  called  refracting  telescopes.     Some- 
times the  first  image  is  made  by  a  concave  mirror,  and  is 


LIGHT. 


207 


then  viewed  by  an  eye-piece,  as  in  the  case  of  the  other. 
These  are  reflecting  telescopes.  One  form  of  them  is  seen  in 
Fig.  219. 

Here  also  the  first  image  is  inverted.     In  case  it  is  de- 
sired to  see  things  erect,  as  in  a  terrestrial  telescope  or  a 


FIG.  219.— PRINCIPLE  OF  THE  REFLECTING  TELESCOPE. 

spy-glass,  another  lens  is  added,  to  reinvert  the  image. 
Two  lenses  are  found  to  answer  better  than  one  for  the 
eye-piece.  Also  in  a  terrestrial  glass  four  lenses  are  used 
instead  of  two. 

335.  Opera-Glasses. — The  first  telescope  ever  made — Gali- 
leo's— was  a  combination  of  a  convex  objective  with  a  con- 


FIG.  220.— PRINCIPLE  OF  THE  OPERA-GLASS. 


cave  eye-piece.  The  latter  was  placed  so  as  to  intercept 
the  rays  before  they  reached  the  focus,  so  that  no  image 
was  formed  by  the  objective.  An  apparent  image  was 


208 


NATURAL  PHILOSOPHY. 


formed  by  the  eye-piece,  which  was  erect.  This  telescope 
has  a  large  field  of  view,  but  small  magnifying  power,  and 
is  used  in  opera-glasses.  Each  tube  is  such  a  telescope. 

336.  Cause  of  Solidity.  —  Bodies  appear  solid  to  us  because 
we  see  them  with  both  eyes.     With  one  eye  we  see  a  little 
around  one  side,  and  with  the  other  a 
little   around   the  other.      These  two 
pictures  give  the  appearance  of  solidity. 

Experiment  119.  —  Look  with  one  eye  at  ob- 
jects of  which  you  do  not  know  the  shape,  and 
notice  how  flat  they  appear.  Notice,  also,  how 
difficult  it  is  to  judge  of  distance  with  one  eye 
shut,  by  attempting  to  place  the  finger  on  the 
object.  With  one  eye  shut,  endeavor  to  place 
against  each  other  two  pencil-points  at  arms'- 
length. 

337.   Stereoscope.  —  The   stereoscope 
is  constructed  on  this  principle.     Two 
pictures  of  an  object  are  taken  from 
slightly-different  positions.     These  are 
placed   so   that  the   light  from   them 
after  passing  through  glasses  appears  to  throw  them  into 
the  same  position.     The  points  of  difference  in  the  two 


Fm-  ^ 


FIG.  222. — PRINCIPLE  OF  THE  PROJECTING  LANTERN. 

pictures  are  brought  out  and  blended  together,  giving  the 
effect  of  solidity. 

338.  Projecting  Lantern. — A  projecting  lantern  is  often 
used  for  lecture  and  educational  purposes  for  throwing  pic- 
tures on  a  screen  in  front  of  the  audience.  A  light,  usually 


LIGHT.  209 


composed  of  a  burning  stream  of  house-gas  and  oxygen 
playing  upon  a  piece  of  quick-lime,  is  contained  in  an 
opaque  box.  In  the  front  part  of  this  box  are  one  or  two 
double-convex  lenses,  which  bring  the  rays  to  a  focus.  In 
front  of  this  lens  is  placed  the  picture  to  be  exhibited.  An 
image  of  this,  real  and  inverted,  is  then  thrown  on  the 
screen  by  another  combination  of  lenses.  The  size  of  the 
image  depends  on  the  distance  of  the  screen  from  the 
lantern. 

339.  The  Camera. — The  camera  used  by  photographers 
is  a  dark  chamber  with  a  convex  lens  in  front  and  a  screen 
at  the  back.     The  lens  produces  on  the  screen  an  image 
of  the  objects  in  front  of  it.     The  screen  is  ground  glass, 
semi-transparent,  so   that   the   image   can  be   seen  from 
behind.     When  this  image  is  made  clear  by  careful  focus- 
ing, the  lens  is  covered,  the  sensitive  plate  is  put  in,  and 
exposed  by  uncovering  the  lens. 

340.  The  Eye. — The  eye  is  an  instrument  in  optical  prin- 
ciples nearly  the  same  as  the  camera.     It  consists  of  a  ball 
surrounded  with  a  strong,  firm  coat,  the  sclerotic  coat, — the 
"  white  of  the  eye," — except  a  little  space  in  front,  where 
there  is  a  transparent  coat,  the  cornea.  Inside  the  sclerotic  is 
the  choroid  coat,  of  dark  color,  to  quench  the  scattering  rays ; 
this  is  seen  through  the  pupil  of  the  eye.     Inside  of  this, 
again,  is  the  retina.     Back  of  the  cornea  is  a  chamber  filled 
with  a  transparent  liquid,  the  aqueous  humor.     Behind  this, 
again,  is  the  iris,  a  mass  of  radiating  fibres,  which  by  their 
expansion  and  contraction  change  the  size  of  the  hole  in 
the  centre,  the  pupil,  and  also  give  the  color  to  the  eye. 
Back  of  this  is  the  .crystalline  lens,  a  double-convex  lens  of 
cartilage,  held  in  place  by  muscles.    Back  of  the  crystalline 
lens,  and  filling  the  main  body  of  the  eye,  is  the  vitreous 
humor.     The  rays  of  light  from  external  objects  are  made 
slightly  more  convergent  by  the  cornea,  and  are  brought  to 
a  focus  on  the  retina  by  the  crystalline  lens,  forming  a  real 
and  inverted  image  there.     The  impression  of  this  image 


210 


NATURAL  PHILOSOPHY. 


conveyed  to  the  brain  by  the  optic  nerve  gives  the  sensa- 
tion of  sight.     Each  eye  forms  its  own  image,  as  in  the 


N 


FIG.  223.— THE  HUMAN  EYE. 

FIG.  223.— THE  HUMAN  EYE.  A,  cornea;  B,  aqueous  humor;  C,  pupil :  D,  iris;  E,  crys- 
talline lens;  H,  sclerotic  coat;  I,  choroid  coat;  K,  retina;  L,  vitreous  humor; 
M,  optic  nerve ;  N,  0,  P,  muscles. 

stereoscope :  these  images  are  slightly  different,  and  their 
blending  gives  the  idea  of  solidity. 

341.  Defects  in  the  Eye. — When  the  image  is  clear  and 
distinct  on  the  retina,  the  impression  is  clear  and  distinct. 
If,  through  any  error  of  curvature  of  the  cornea  or  crys- 
talline lens,  the  image  is  not  made  exactly  on  the  retina, 
sight  is  not  perfect.  If  the  image  is  formed  in  front  of  the 
retina,  the  person  is  short-sighted;  if  it  is  intercepted  by 
the  retina  before  reaching  a  focus,  the  person  is  long-sighted. 
It  is  the  case  of  a  camera  out  of  focus.  The  unconscious 
endeavor  to  focus  the  eye  in  such  cases  produces  straining 
of  the  muscles,  pain,  and  disease.  This  is  corrected  by  the 
use  of  glasses,  either  concave  or  convex.  If  the  person  is 
long-sighted,  a  convex  lens  is  put  in  the  spectacles,  to  assist 


LIGHT.  211 


the  crystalline  lens  in  bringing  the  object  to  a  focus  on  the 
retina;  if  short-sighted,  a  concave  lens,  to  overcome  the 
effect  of  the  too  great  convexity  of  the  crystalline. 

342.  Focus  of  the  Eye.  —  As  rays  from  a  near  object  do  not 
come  in  so  nearly  parallel  as  if  the  object  were  distant,  the 
muscles  have  the  power  to  change  the  curvature  of  the 
crystalline  lens  to  suit  the  differing  distances.    This  is  done 
without  effort  on  our  part,  and,  unless  continued  so  long  as 
to  tire  the  muscles,  without  any  inconvenience.     The  eye 
can  immediately  turn  from  reading  a  book  to  look  at  the 
distant  horizon  without  effort  or  pain,  though  it  involves 
considerable  changes  in  the  curvature  of  the  lens. 

Experiment  120.  —  Procure  an  eye  of  an  ox  or  other  animal,  freeze 
it,  and  cut  it  into  two  from  front  to  back  with  a  razor.  Notice  the 
various  parts  described  above. 

343.  Persistence  of  Impressions.  —  An  impression  on  the 
retina  is   not   immediately  effaced,  but   after  the  object 
creating  it  is  removed,  it  will  still  remain  a  few  seconds. 
If  a  stick  with  a  glowing  coal  on  it  be  whirled  around,  a 
whole  circle  of  light  can  be  seen.     Experiment  111  is  also 
explained  by  this.     The  different  colors  are  mixed  in  the 
eye,  and  white  is  produced. 

344.  Inversion  of  the  Image.  —  The  image  is  inverted  on 
the  retina  by  the  convex  crystalline  lens,  but  the  impres- 
sion is  rearranged  in  the  optic  nerve  or  in  the  brain.     An 
image  is  seen  in  both  eyes,  but  these  are  combined  into 
one,  except  in  the  case  of  an  object  too  close  for  distinct 
vision,  or  in  other  abnormal  cases. 

345.  Blind  Spot,  —  The  part  of  the  retina   immediately 
over  the  end  of  the  optic  nerve  does  not  transmit  its  im- 
pressions to  the  brain.     This  is  the  "  blind  spot"  of  the  eye. 
Its  presence  may  be  shown  as  follows. 

Experiment  121.  —  Make  three  heavy  circles,  as  below.     Close  the 


left  eye,  and  hold  the  left  spot  in  front  of  the  right  eye  ;  look  at  it 


212  NATURAL  PHILOSOPHY. 


intently.  By  moving  the  paper  slightly  right  and  left  a  place  can  be 
found  where  the  left  spot  will  be  visible  and  not  the  centre  one.  Its 
image  falls  on  tlie  blind  spot. 

General  Exercises. — 1.  Suppose  a  coin  an  inch  in  diameter  to  be 
held  up  before  a  wall  parallel  to  it ;  let  the  distance  of  the  coin  from 
the  source  of  light  be  15  inches,  and  that  of  the  wall  from  the  source 
5  feet:  show  that  the  area  of  the  shadow  is  1G  times  that  of  the  coin. 

2.  Show  that  if  light  takes  three  years  to  pass  trom  a  star  to  the 
earth,  that  star  is  nearly  200,000  times  more  distant  from  the  earth 
than  the  sun  is. 

3.  If  the  weight  of  a  molecule  of  light  amounted  to  but  one  grain, 
show  that  its  momentum  would  be  about  equal  to  that  of  a  cannon- 
ball  weighing  150  pounds  and  moving  with  the  velocity  of  1000  feet 
in  a  second. 

4.  Show  at  what  angle  a  ray  must  be  incident  on  a  plane  reflecting 
surface  in  order  that  the  reflected  ray  may  make  a  right  angle  with 
the  incident  ray.     Ans.  45°. 

5.  Find  the  angle  between  two  plane  reflectors  so  that  a  ray  origi- 
nally parallel  to  one  of  them  may,  after  two  reflections,  be  parallel 
to  the  other.     Ans.  60°. 

6.  A  man  stands  upright  before  a  plane  vertical  reflector,  and 
observes  that  he  cannot  see  the  image  of  his  head  or  of  his  feet : 
show  that  if  he  goes  nearer  to  the  reflector  or  farther  from  it  he  can 
still  see  only  the  same  portion  of  his  image  as  before. 

7.  A  man  stands  before  a  looking-glass  of  his  own  height :  show 
that  he  can  see  his  whole  image,  and  determine  how  much  of  the 
looking-glass  is  concerned  in  the  formation  of  the  image. 

8.  The  sun  is  30  degrees  above  the  horizon,  and  his  image  is  seen 
in  a  tranquil  pool :  determine  in  this  case  the  angle  of  incidence  and 
reflection. 

9.  A  man  stands  before  a  looking-glass  with  one  eye  shut,  and 
covers  its  place  on  the  glass  with  a  wafer :  show  that  the  same  wafer 
will  hide  the  other  eye  as  soon  as  it  is  shut  and  the  first  is  opened. 

10.  A  small  object  is  placed  half-way  between  the  centre  and  the 
principal  focus  of  a  concave  reflector :  draw  the  image,  and  show  in 
what  proportion  it  is  to  the  object. 

11.  State  what  would  be  the  appearance  of  a  man  standing  on  the 
brink  of  a  lake  to  an  eye  under  the  water. 

12.  The  rays  of  the  sun  are  received  on  a  large  converging  lens, 
the  focus  being  rendered  visible  by  the  dust  floating  in  the  air ;  a 
screen  placed  a  little  in  front  of  the  focus  shows  a  white  circle  sur- 
rounded by  a  red  fringe,  and  placed  a  little  behind  the  focus  shows  a 
white  circle  surrounded  by  a  blue  fringe :  explain  this. 

13.  A  window-bar  is  viewed  through  a  prism,  the  edge  of  which  is 
parallel  to  the  bar :  show  that  the  side  of  the  bar  which  is  nearer  to 
the  edge  of  the  prism  is  fringed  with  red  and  orange,  and  the  other 
side  with  violet  and  blue. 


HEAT.  213 


CHAPTEE    VII. 

HEAT. 

346.  What  is  Heat  ?— Heat,  like  light,  consists  of  waves 
of  ether.     The  waves  of  heat  cannot  be  seen  by  the  eye ; 
they  can  be  felt  by  the  nerves  of  sensation,  which  are 
scattered  over  the  whole  surface  of  the  body. 

Heat  is,  then,  a  mode  of  motion.1  When  a  body  is  heated 
its  particles  are  set  in  vibration.  This  vibration  is  then 
communicated  to  the  ether  which  is  in  contact  with  them, 
and  so  is  conveyed  to  the  senses.  As  the  temperature  is 
raised,  the  vibrations  become  more  and  more  rapid,  till  after 
a  while  they  have  such  rapidity  that  they  are  capable  of 
being  perceived  by  the  eye,  and  the  body  is  seen  to  glow. 

347.  Theories  of  Heat. — There  was  an  old  theory  that 
heat  was  caused  by  the  passage  of  particles  of  matter  from 
the  heated  body.     But  this  seems  to  be  now  disproved. 
The  present  theory  of  heat  is  called  the  undulatory  theory. 

348.  Sources  of  Heat. — The  sources  of  heat  are  in  general 
the  same  as  the  sources  of  light.     The  great  reservoir  is 
the  sun.     It  is  constantly  giving  it  out  to  the  earth :  the 
earth  uses  some  of  it  up,  and  some  it  radiates  again  into 
space.     An  immense  amount  of  heat  is  received  even  in 
the  frigid  regions  from  the  sun.     Were  it  not  for  this,  the 
temperature  of  the  whole  earth  would  be  far  below  zero 
continually. 

1  Prof.  Tyndall  has  written  a  book  called  "Heat  a  Mode  of  Motion." 
This  is  an  excellent  treatise  on  the  subject,  and  will  give  to  students  a 
valuable  lesson  in  the  careful  habits  which  are  necessary  to  a  scientific 
investigator. 


214  NATURAL   PHILOSOPHY. 

349.  Chemical  Action  a  Source  of  Heat. — Chemical  action 
is  another  source  of  heat. 

Experiment  122. — Mix  some  strong  sulphuric  acid  and  water  slowly 
together,  stirring  the  mixture.  They  combine,  and  the  vessel  is 
heated.  A  thermometer  will  show  the  rise  in  temperature.1 

The  heat  from  combustion  is  from  this  source.  There  is 
a  chemical  union  between  the  oxygen  of  the  air  and  the 
carbon  and  hydrogen  of  the  combustible.  A  certain  amount 
of  heat  is  necessary  to  start  this  action,  but  when  started 
it  keeps  itself  going  by  the  heat  which  it  generates. 

Experiment  123. — Put  some  "quick-lime"  in  water;  apply  the 
thermometer  to  the  water  before  and  after.  There  is  here  chemical 
union  between  the  lime  and  the  water,  and  "  slaked  lime"  is  formed. 

350.  Stoppage  of  Motion  a  Source  of  Heat, — The  stoppage 
of  motion  is  a  great  source  of  heat. 

Experiment  124. — Lay  a  nail  on  an  anvil,  and  strike  it  two  or  three 
sharp  blows  with  a  hammer.  Then  quickly  touch  the  nail  to  a  little 
piece  of  phosphorus,  or,  if  this  is  not  to  be  had,  give  it  more  strokes 
and  touch  it  to  the  head  of  a  match.  The  phosphorus  or  the  match 
will  take  fire. 

We  say  the  motion  is  converted  into  heat.  This  means  that 
the  motion  of  the  hammer  is  changed  into  the  vibratory 
motion  of  the  particles  of  the  nail,  which  in  turn  commu- 
nicates itself  to  the  particles  of  the  phosphorus.  It  is  an 
illustration  of  the  correlation  of  forces. 

351.  Illustrations  of  the  Conversion  of  Motion  into  Heat. 
— There  are  many  illustrations  of  the  conversion  of  motion 
into  heat.     Meteors,  or  "shooting-stars,"  are  little  stones 
which  enter  our  atmosphere  with  great  velocity.     They 
strike  so  many  particles  of  air,  and  so  much  of  their  motion 
is  stopped,  that  they  become  intensely  hot,  and  finally  burn 
up,  giving  out  the  light  by  which  we  see  them.     All  fric- 
tion is  accompanied  by  heat,  for  a  similar  reason.     It  is 
the  stoppage  of  motion.     Friction-matches,  the  heating  of 


1  For  this  and  similar  experiments  a  thermometer  should  be  pro- 
cured without  a  frame,  and  with  the  markings  on  the  tube. 


HEAT.  215 


axles,  the  Indian  habit  of  rubbing  two  sticks  together  or 
of  striking  flints  to  light  a  fire,  rubbing  the  hands  to  warm 
them,  are  illustrations. 

352.  It  is  believed  that  the  heat  of  the  sun  is  partly 
supported  by  the  fall  of  bodies  into  it  and  the  conversion 
of  their  motion  into  heat.     As  we  know  that  the  sun  is 
continually  expending  its  energies  in  all  directions  into 
space,  we  must  explain  in  some  way  its  sustenance,  and 
the  heat  generated  by  the  fall  of  bodies  from  some  dis- 
tance away  would  be  many  times  greater  than  that  which 
would  be  produced  by  their  combustion  were  they  com- 
posed of  solid  coal.1 

353.  Mechanical  Equivalent  of  Heat.— A  given  amount 
of  motion  stopped  will  always  produce  the  same  amount 
of  heat.     The  amount  of  motion  in  a  body  depends  on  two 
things, — the  mass  and  the  velocity, — and  is  measured  in 
foot-pounds.      To  raise  one  pound  of  water  through  one 
degree   Fahrenheit   requires   772   foot-pounds   of   motion 
stopped.     If  a  pound-weight  could  fall  into  a  pound  of 
water  from  a  height  of  772  feet,  and  all  the  heat  resulting 
could  be  collected  in  the  water,  its  temperature  would  be 
raised  one  degree  Fahrenheit. 

This  number  772  is  called  the  mechanical  equivalent  of 
heat,  and  was  determined  by  Joule x  in  a  number  of  ways, 
one  of  which  was  the  following.  He  had  a  box  of  water  in 
which  were  a  number  of  paddles  which  churned  the  water. 
These  paddles  were  turned  by  a  weight  falling.  The 
weight  being  known,  and  the  space  through  which  it  fell, 
also  the  difference  of  temperature  of  the  water  at  the  be- 
ginning and  at  the  end  of  the  fall,  the  amount  of  fall  neces- 
sary to  produce  an  increase  of  1°  was  easily  calculated. 
Thus,  a  100-pound  weight  falling  through  20  feet  would 
perform  2000  units  of  work.  If  this  raised  the  temperature 

1  See  Sharpless  and  Philips 's  "  Astronomy,"  Art.  47. 
3  James  P.  Joule  (jool),  an  English  physicist,  1818-. 


216 


NATURAL   PHILOSOPHY. 


of  one  pound  of  water  2.59°,  then  to  raise  it  1°  there 
would  be  2000  -f-  2.59  =  772.2  units  of  work  expended. 


FIG.  224. — JOULE'S  MACHINE. 

354.  Conservation  of  Energy. — If  now  this  heat 
could  all  be  utilized  in  an  engine,  it  could  just 
lift  the  weight  to  the  point  from  which  it  fell. 
We  have  another  illustration  of  the  "  conserva- 
tion of  energy."     The  mechanical  motion  is  de- 
stroyed, but  an  equivalent  in  molecular  motion 
(heat)  is  produced.     A  certain  amount  of  me- 
chanical   motion    always    produces    the    same 
amount  of  heat,  and  if  this  could  all  be  collected 
it   would    in    turn    reproduce    the    mechanical 
motion.    The  energy  is  not  lost,  but  is  converted 
into  another  form.     Heat  is  converted  into  me- 
chanical motion  in  locomotives.    This  goes  again 
into  heat  in  the  friction  of  the  bearings  of  the 
different  axles  of  the  train,  of  the  wheels  against 
the  track,  and  of  the  train  against  the  air. 

355.  Thermometers. — Temperature  is  measured 
by  thermometers.     The  most  common  thermometer  is  the 


FIG.  225.— 
THERMOME- 
TER. 


HEAT. 


217 


mercury  thermometer,  and  it  depends  upon  the  principle 
that  heat  expands  the  mercury  in  a  tube  and  cold  causes  it 
to  contract.  It  consists  of  a  bulb  with  a  tube  attached. 
The  bulb  and  part  of  the  tube  are  filled  with  mercury,  and 
the  remainder  contains  no  air,  but  only  a  little  vapor  of 
mercury.  To  construct  a  thermometer  the  mercury  is 
heated  in  the  bulb,  and  when  the  tube  is  full  of  vapor  it  is 
sealed  up  at  the  upper  end.  Then  in  cooling  most  of  the 
vapor  condenses  and  leaves  nearly  a  vacuum  in  the  upper 
part  of  the  tube. 


FIG.  226.  — To  FIND  THE 
FREEZING-POINT  OF  A 
THERMOMETER. 


FIG.  227.— To  FIND  THE  BOILING-POINT  OF  A  THER- 
MOMETER. 


356.  Freezing-Point  and  Boiling-Point. — There  are  several 
ways  of  graduating  thermometers,  but  in  all  there  are 


19 


218  NATURAL   PHILOSOPHY. 

two  points  which  must  be  determined.  These  are  the 
freezing-point  of  water  and  the  boiling-point  of  water. 

To  determine  the  first,  the  bulb  is  kept  in  a  mass  of 
chopped  ice  or  snow  till  the  mercury  settles  at  a  definite 
place.  This  place  is  then  marked. 

To  determine  the  boiling-point,  the  bulb  is  placed  in 
boiling  water,  from  which  the  steam  is  allowed  to  pass 
freely  and  to  envelop  the  tube.  The  point  at  which  the 
mercury  settles  is  then  also  marked. 

357.  Graduation.  —  We  have  now  two  marks,  and  it  is 
necessary  to  graduate   the   thermometer   between   them. 
There  are  two  common  methods  of  doing  this. 

358.  Centigrade  Thermometers.  —  The  first  is  the  Centi- 

grade method,  used  in  France,  and  by  scien- 
•100  -  -212  tific  people  everywhere.  The  freezing-point 
is  marked  0°,  and  the  boiling-point  100°,  and 
the  space  between  is  divided  into  100  equal 
divisions.  Divisions  of  the  same  size  are 
then  continued  above  100°  and  below  0°  as 

^ar  as  necessary- 

359.  Fahrenheit  Thermometers.  —  The  other 
is  the  Fahrenheit  method,  used  by  people  in 
general  in  England  and  the  United  States. 
FIG.  228.-CENTI-  The   freezing-point   is   marked  32°,  and  the 

G  BADE         AN  D  ol  ' 

FAHRENHEIT  boiling-point  212°,  and  the   space  between  is 

THERMOMETERS. 

divided  into  180  equal  divisions,  which  are 
continued  up  and  down.  Both  methods  will  be  used  in 
this  treatise,  the  addition  of  the  letter  C.  or  F.  stating 
which. 

As  100°  C.  are  equivalent  to  180°  F.,  5°  C.  are  equivalent 
to  9°  F.  ;  hence  any  number  of  degrees  of  one  scale  can  be 
reduced  to  its  corresponding  number  of  the  other. 

Exercises.  —  1.  To  what  marking  on  F.  scale  does  40°  C.  corre- 
spond ? 

Since  5°  C.=9°  F., 

1°  C.  r=f°  F., 

and  40°  C.  =  72°  F. 


—17  s  -  - 


HEAT.  219 


This  gives  the  number  of  F.  degrees  above  freezing-point,  which 
is  32°  above  zero.  Then  the  reading  of  the  F.  scale  would  be  104°. 

2.  To  what  marking  on  C.  scale  does  122°  F.  correspond  ?     Ans. 
50°. 

3.  To  what  marking  on  F.  scale  does  10°  C.   correspond  ?    Ans. 
+50°. 

4.  To  what  marking  on  C.  scale  does  — 40°  F.  correspond  ?      Ans. 
—40°. 

5.  How  many  units  of  work  are  required  to  raise  1  pound  of  water 
through  1°  C.  ?     Ans.  About  1390. 

360.  Unit  of  Heat. — It  is  convenient  to  have  some  unit 
by  which  to  measure  the  amount  of  sensible  heat  in  a  body. 
The  unit  adopted  is  the  amount  of  heat  required  to  raise  the 
temperature  of  one  pound  of  water  at  32°  through  one  degree. 

361.  Specific   Heat. — If  instead  of  taking  a  pound  of 
water  we  take  a  pound  of  mercury  and  expose  it  to  the 
same  heat,  its  temperature  will  rise  more  than  that  of  water. 
More  of  the  heat  given  to  the  water  is  employed  in  keep- 
ing the  molecules  in  vibration  than  in  the  case  of  the  mer- 
cury, so  that  it  does  not  show  itself  by  a  thermometer.    All 
known  substances  except  hydrogen  will  rise  in  tempera- 
ture farther  than  water  by  the  application  of  the  same 
amount  of   heat.     The  specific  heat  of  a  substance  is  the 
amount  of  heat  necessary  to  raise  one  pound  of  it  through  one 
degree,  the  specific  heat  of  water  being  1. 

One  way  of  determining  the  specific  heat  of  a  substance 
is  by  the  method  of  mixtures. 

Experiment  125.— Mix  together  one  pound  of  water  at  80°  and 
one  pound  at  50°.  The  mixture  will  be  at  65°.  The  former  loses  as 
much  as  the  latter  gains. 

Experiment  126. — Mix  one  pound  of  water  at  80°  with  one  pound 
of  mercury  at  50°.  The  mixture  will  be  at  79°.  The  water  has  lost 
1°,  and  that  has  raised  the  mercury  through  29°.  The  specific  heat 
of  mercury  is  therefore  ^. 

362.  Heat  produces  Expansion. — The  general  effect  of 
heat  is  to  expand  bodies.     An  iron  ball  that  will  just  pass 
through  a  ring  when  cold,  is  too  large  when  hot.     An  iron 
rod  will  measure  a  little  longer  when  heated.     The  rails 
of  a  track  laid  in  summer  will  be  separated  in  winter. 

The  expansion  is  accomplished  by  the  separation  of  the 


220 


NATURAL   PHILOSOPHY. 


molecules,  and  the  separation  is  caused  by  their  rapid  vi- 
bration. This  requires  more  room,  and  overcomes  to  some 
extent  the  force  of  cohesion.  The  force  of  separation  is  so 


FIG.  229.— EXPANSION  OF  SOLIDS  BY  HEAT.    FIG.  230.— EXPANSION  BY  HEAT.— GBIDIBON 

PENDULUM. 

great  that  it  is  generally  useless  to  try  to  counteract  it. 
In  iron  buildings  and  bridges  arrangements  are  made  so 
that  the  pieces  can  be  allowed  to  expand  without  injury. 

363.  Melting  and  Evaporation  by  Heat. — As  the  heat  is 
increased,  the  particles  are  more  and  more  agitated  and  dis- 
persed, and  the  force  of  cohesion  becomes  less  and  less,  until 
finally  the  body  changes  from  a  solid  to  a  liquid.  If  heat 
is  still  applied  to  it,  the  molecules  are  farther  separated, 
until  they  reach  such  a  distance  apart  that  no  cohesive 
force  acts  between  them,  and  the  liquid  becomes  a  gas. 


HEAT. 


221 


Melting  and  evaporation,  then,  must  be  considered  as  the 
shaking  apart  of  the  molecules  by  the  vibratory  motion 
communicated  to  them,  which  vibratory  motion  is  heat. 


FIG.  231.— EXPANSION  OF  LIQUIDS  BY  HEAT. 


FIG.  232. — EXPANSION  OF  AIR. 


364.  Expansion  of  Liquids. — The  expansion  of  liquids  can 
be  readily  seen  by 

Experiment  127.— Partly  fill  with  colored  liquid  a  glass  tube  with 
a  bulb.  Immerse  the  bulb  in  water,  and  apply  heat  gently.  The 
colored  liquid  will  rise  in  the  tube.  Thermometers  are  based  on 
the  principle  of  the  expansion  of  liquids  by  heat. 

19* 


222  NATURAL   PHILOSOPHY. 


365.  Expansion  of  Gases. — The  expansion  of  gases  can  be 
seen  by  the  following : 

Experiment  128. — Heat  a  flask  filled  with  air,  and  conduct  a  tube 
into  a  vessel  of  water.  The  expanded  air  will  be  driven  out  of  the 
tube,  and  will  bubble  up  through  the  water. 

Experiment  129. — Tie  up  a  bladder  or  a  toy  balloon  partly  filled 
with  air.  Heat  it,  and  the  balloon  will  expand. 

In  Experiment  128  it  is  evident  that  the  air  remaining 
in  the  flask  will  weigh  less  after  being  heated  than  did  the 
original,  for  there  are  fewer  particles. 

366.  Law  of  Expansion  of  Gases. — There  does  not  seem 
to  be  any  general  law  which  can  be  said  to  govern  the 
cases  of  expansion  of  solids  and  liquids,  since  they  are  so 
diverse  in  their  qualities.    But  a  true  gas  (not  a  vapor)  will 
expand  according  to  a  certain  law,  whatever  its  composi- 
tion.    If  kept  under  a  constant  pressure  as  it  expands,  it  will 
increase  -%fo  of  its  volume  at  0°  for  every  Centigrade  degree  of 
heat  given  it. 

To  illustrate  this,  suppose  p  to  be  a  piston  fitting  closely 
in  a  tube  ab,  but  moving  up  and  down  without  fric- 
tion, and  suppose  the  portion  pb  below  the  piston  to  be 
filled  with  gas  at  a  temperature  of  0°  C.  If  the  tem- 
perature be  raised  to  1°,  the  gas  will  expand  ^^  of 
its  volume,  and  will  lift  the  piston  ;  if  raised  to  2°,  it 
will  expand  yfg-  of  its  original  volume ;  and  so  on.  If 
raised  to  273°,  it  will  have  just  double  its  original 
volume. 

We  can  also  carry  the  process  the  other  way.  If 
1°  of  heat  be  taken  from  the  gas,  the  resulting  volume 
23?;  will  be  |^|  of  the  original ;  if  2°,  |^J ;  and  so  on  down. 
In  theory,  when  the  gas  is  cooled  to  — 273°  it  would 
have  no  volume  at  all.  But  practically  it  becomes  a  solid 
long  before  it  reaches  this  temperature,  and  the  law  does  not 
apply  to  solids.  This  number,  — 273°  Centigrade,  is  called 
the  absolute  zero  of  temperature. 

What  would  be  the  absolute  zero  on  F.  scale  ? 


HEAT.  223 


367.  Relation  between  Heat  and  Volume.— When  a  body 
is  heated,  some  of  the  heat  goes  to  expand  it,  so  that  the 
temperature  is  not  so  great  as  it  would  otherwise  be.     If 
the  piston  in  Fig.  233  were  held  down  so  that  the  gas  could 
not  expand,  the  same  amount  of  heat  applied  to  it  would 
raise  its  temperature  higher.     In  expanding,  part  of  the 
heat  is  used  up  in  doing  the  work  of  separating  the  mole- 
cules.    This  heat  is  consumed  continuously  in  keeping  the 
molecules  apart,  and  any   abstraction  of  heat  will  allow 
them  to  come  together  again.     Hence  cold  produces  con- 
traction.    Cooling  is  the  loss  of  vibratory  motion,  and  as 
the  motion  ceases,  the  molecules  approach  one  another. 

.N~ow,  if  the  expansion  is  produced  by  a  force,  without 
the  application  of  any  external  heat,  cold  is  produced.  For 
part  of  the  heat  previously  in  the  body  is  now  consumed  in 
maintaining  the  separation  of  the  molecules.  The  sudden 
stretching  of  a  wire  lowers  its  temperature.1 

368.  Heat  and  Fusion, — When  heat  is  applied  to  a  solid 
body  so  as  to  raise  its  temperature  to  the  point  of  fusion 
or  melting,  the  addition  of  more  heat  will  not  further  raise 
the  temperature  till  the  body  is  completely  melted.     The 
heat  does  the  work  of  driving  the  molecules  apart,  and  so 
changing  it  from  solid  to  liquid.     A  certain  amount  of  heat 
is  consumed  in  maintaining  the  liquid  form. 

Experiment  130. — Place  a  piece  of  ice  in  a  vessel  over  a  slow  fire. 
As  the  ice  melts,  keep  it  well  stirred,  and  frequently  apply  a  thermom- 
eter. It  will  indicate  the  freezing-point  until  all  the  ice  is  melted. 

Although  much  heat  has  gone  into  the  ice,  it  has  been 
destroyed  as  sensible  heat,  and  is  employed  in  keeping  the 
molecules  at  such  a  distance  from  one  another  as  to  make  a 
liquid.  This  energy,  which  does  not  show  itself  by  a  ther- 
mometer, is  called  latent  heat  It  requires  80  units  of  heat 
to  melt  ice,  or  as  much  as  would  raise  the  same  weight  of 

1  India-rubber  seems  to  be  an  exception  to  both  laws.  "When 
stretched,  heat  is  produced,  and  the  application  of  heat  contracts  in- 
stead of  expanding  it. 


224  NATURAL   PHILOSOPHY. 


water  through  about  80°  C.  of  temperature.     When  the  ice 
freezes,  the  same  amount  of  heat  is  given  out. 

Melting,  then,  implies  the  using  up  of  heat.  As  this  heat 
comes  from  external  sources,  its  effect  is  to  reduce  their 
temperature.  Freezing,  on  the  contrary,  liberates  heat 
and  raises  the  temperature  of  surrounding  objects.  Melting 
causes  cold,  and  freezing  causes  heat. 

Experiment  131. — Mix  some  chopped  ice  with  salt,  and  stir  well 
together,  and  keep  a  thermometer  in  the  mixture.  It  will  indicate  a 
temperature  much  below  the  freezing-point.  The  salt  makes  the  ice 
melt,  and  so  causes  cold.  This  is  the  common  freezing  mixture  used 
by  ice-cream-makers. 

Experiment  132. — Pulverize  some  nitrate  of  ammonium  in  a  thin 
glass  vessel,  add  water,  and  stir.  As  the  salt  dissolves,  insert  the  bulb 
of  a  thermometer.  The  mercury  will  rapidly  fall.  Place  the  vessel 
on  a  wet  board.  It  will  freeze  to  it. 

Here  the  rapid  solution  of  the  salt  in  water  abstracted 
heat  from  the  vessel,  from  the  thermometer,  and  from  the 
board.  Hence  not  only  fusion,  but  solution,  causes  cold. 

Define  fusion  and  solution. 

369.  Heat  and  Evaporation. — Similar  effects  are  seen  in 
the  passage  from  the  liquid  to  the  gaseous  state.     Heat  is 
required  to  keep  up  the  gaseous  condition  of  a  body :  hence 
evaporation  takes  heat  from  surrounding  objects  and  causes 
cold,  and  condensation  liberates  it  and  raises  temperature. 

Experiment  133. — Pour  a  little  ether  in  the  palm  of  the  hand.  As 
it  rapidly  evaporates,  considerable  cold  is  felt.  Dip  a  thermometer  in 
ether  and  quickly  remove  it.  The  ether  which  adheres  will  evaporate 
and  take  heat  from  the  mercury  in  the  bulb. 

370.  Freezing  in  Red-Hot  Vessels.— Sulphurous  acid — 
the  gas  formed  when  sulphur  is  burned  in  air — is  capable 
of  being  made  liquid  by  passing  it  through  a  tube  immersed 
in  a  freezing  mixture  of  ice  and  salt.   If  a  crucible  be  heated 
red-hot,  a  little  water  put  in  it,  and  immediately  the  liquid 
sulphurous  acid  poured  on  it,  so  great  a  degree  of  cold  will 
be  produced  by  the  sudden  vaporization  of  the  acid  that 
the  water  will  be  frozen  in  the  red-hot  crucible. 

371.  Solidification  of  Gases.— If  a  gas  be  condensed  by 


HEAT.  225 


great  cold  and  pressure,  and  then  suddenly  be  allowed  to 
expand  by  passing  out  through  a  fine  tube,  the  great  expan- 
sion and  evaporation  will  cause  such  cold  that  the  gas  will 
be  liquefied,  and  in  some  cases  solidified.  Hydrogen,  the 
lightest  of  all  gases,  has  been  made  solid  by  this  method, 
and  been  heard  to  rattle  on  the  floor  like  minute  hailstones. 

372.  Cryophorus. — A  cryophorus  is  an  instrument  con- 
sisting  of  two    glass    bulbs    connected    as    in   Fig.   234. 
One  of  these  is  partly  filled 

with   water,  and   the   rest 

of  the  apparatus  is   made 

as    nearly    as     possible    a 

vacuum.    This  is  soon  filled 

with  vapor  of  water,  which  FIG.  234.— CEYOPHORUS. 

passes   oif  under  the   low 

pressure.     If  the  other  bulb  is  placed  in  a  freezing  mixture 

of  ice  and   salt,  the  vapor  is  condensed,  and  evaporation 

goes  on  so  rapidly  from  the  water  that  it  finally  freezes. 

373.  Artificial  Ice. — In  India,  ice  is  made  by  putting 
water  into  pots  of  porous  earthenware.     The  water  evap- 
orates from  the  outside  of  these  so  as  to  freeze  the  water 
on  the  inside.     Artificial  ice  is  produced  in  warm  coun- 
tries on  a  large  scale  by  passing  liquid  ammonia  through 
pipes  which  line  the  bottom  and  sides  of  a  vessel  of  water. 
The  liquid  is  quickly  converted  into  a  gas,  and  this  takes 
so  much  heat  from  the  water  that  it  is  frozen. 

Experiment  134. — Heat  some  water,  having  the  bulb  of  a  ther- 
mometer in  it  during  the  operation.  The  mercury  will  gradually 
rise  till  it  reaches  the  boiling-point ;  after  which,  if  the  steam  is  not 
confined,  it  will  not  indicate  any  higher  temperature  till  the  water  is 
boiled  away. 

374.  Heat  and  Evaporation. — In  this  experiment  the  heat 
applied  after  the  water  commenced  to  boil  is  all  expended 
in  changing  the  liquid  to  a  gaseous  form,  and  becomes  latent 
in  the  gas.     To  change  water  into  vapor  requires  about 
537  times  as  much  heat  as  would  raise  the  same  amount 
through  one  degree  of  temperature, — in  other  words,  537 

P 


226  NATURAL  PHILOSOPHY. 

units  of  heat.  This  number  537  is  called  the  latent  heat 
of  steam,  as  80  (see  Par.  368)  is  the  latent  heat  of  water. 
They  represent  the  number  of  degrees  of  heat  stored  up 
and  kept  in  constant  use  in  maintaining  the  condition  of 
the  body,  and  which  will  not  show  itself  by  a  thermometer. 

375.  Heat  expended  in  Fusion  and  Evaporation.  —  To 
show  the  meaning  of  these  figures,  let  us  suppose  a  mass 
of  ice  at  a  temperature  of  — 10°  C.,  and  let  it  be  heated 
from  a  source  which  gives  it  1°  a  minute.     In  10  minutes 
it  will  be  brought  to  0°.     In  80  minutes  more  it  will  be 
all  melted,  but  it  will  still  be  at  0°.     In  100  minutes  more 
it  will  be  raised  to  a  temperature  of  100°,  and  will  begin 
to  boil.     In  537  minutes  more  it  will  all  be  converted  into 
vapor  at  a  temperature  of  100°.     This  vapor  can  then  be 
increased  in  temperature  by  the  application  of  heat. 

Exercises. — 1.  Why  does  moist  clay  contract  when  heated? 

2.  Why  do  telegraph-wires  hang  down  more  in  summer  than  in 
winter  ? 

3.  Why  does  a  wheelwright  put  the  tire  on  the  wheel  hot? 

4.  Will  sugar  placed  in  coffee  cool  it  more  than  the  same  amount 
of  sand  at  the  same  temperature  ?  why  ? 

376.  Expansion  by  Freezing1. — The  general  effect  of  cold 
is  to  contract.     There  are  exceptions  to  this  in  the  case 
of  water  under  certain  circumstances,  and  of  a  few  other 
substances.     When  water  is  reduced  in  temperature  it  con- 
tracts in  volume  till   it  reaches  the  temperature  of  39° 
F.  or  4°  C.,  after  which  it  begins  to  expand.     This  expan- 
sion amounts  to  about  T^  of  its  original  bulk,  and  shows 
itself  in  bursting  vessels  in  which  it  is  contained.     Heavy 
iron  shells  can  be   thus  burst.     Fig.  235  represents  the 
effects  of  this  expansion.     A  large  shell  was  filled  with 
water  and  the  hole  tightly  stopped  by  a  wooden   plug. 
When  it  froze,  the  plug  was  forced  out  with  great  velocity 
and  a  cylinder  of  ice  eight  inches  long  issued  from  the 
hole.     At  another  time  the  shell  split  in  two,  and  a  sheet 
of  ice  was  forced  out. 

This  lightness  of  ice  causes  it  to  float  on  water.     If  it 


SEAT.  227 


continued  to  contract  as  it  cooled,  it  would  sink,  and  all  of 
it  would  be  at  the  bottom  of  the  ponds. 


FIG.  235. — EFFECTS  OF  FREEZING. 

377.  Freezing. — Freezing  is  the  formation  of  crystals. 
They  begin  to  form  around  the  edge  of  the  pond  or  around 
some  object  floating  in  the  water,  and  add  one  to  another 
till  the  whole  surface  is  frozen.   The  process  can  be  watched 
by  the  following  method. 

Experiment  135. — Wet  a  clear  piece  of  glass  with  a  solution  of 
sulphate  of  copper  or  chloride  of  ammonium,  and  hold  it  between 
you  and  the  light.  In  a  little  while,  as  the  water  dries,  the  crystals 
will  begin  to  shoot  out  in  various  directions  over  the  glass.  The 
effect  is  much  improved  if  the  plate  is  placed  in  a  projecting  lantern 
and  the  formation  of  crystals  shown  on  the  screen. 

378.  Melting, — Melting  is  the  reverse  process  from  freez- 
ing.    When  the  temperature  is  raised  above  the  freezing- 
point  the  crystals   gradually  dissolve   into   water.      This 
goes  on  all  through  the  mass,  and  the  ice  becomes  rotten 
before  it  disappears. 

379.  Evaporation  and  Boiling. — Evaporation  goes  on  at 
all   temperatures.     Ice   is   converted   into  vapor  without 
passing  through  the  intermediate  stage  of  liquids.    Clothes 
hung  out  in  cold  weather  will  become  dry  while  the  tern- 


228 


NATURAL   PHILOSOPHY. 


perature  is  all  the  time  below  the  freezing-point.  But  the 
process  goes  on  the  more  rapidly  the  higher  the  tempera- 
ture. As  water  is  slowly  heated,  steam  passes  away  from 
its  surface  with  greater  rapidity  until,  when  a  certain  tem- 
perature is  reached,  steam  begins  to  form  all  through  its 
mass.  This,  being  lighter  than  water,  is  forced  up  through 
it  to  the  top.  This  is  boiling.  The  heat  being  applied  at 
the  bottom,  that  portion  is  most  heated,  and  steam  is  there 
formed  most  vigorously.  JSTot  only  the  steam  but  also  the 
heated  water,  being  expanded,  rises,  and  the  other  water 
takes  its  place,  to  be  in  turn  heated.  Thus  there  is  a  con- 
stant circulation. 

Experiment  136.— Add  a  little  chalk-dust  from  the  blackboard  to 
water  in  a  glass  flask,  and  heat  it ;  watch  the  circulation  of  the  water 
by  the  aid  of  the  particles  of  dust. 

In  such  experiments 
wipe  the  flask  dry  on  the 
outside,  and  apply  the 
heat  gradually  at  first. 

380.  Relation  of 
Boiling-Point  and 
Pressure.— The  boil- 
ing-point varies  with 
the  pressure.  By  ex- 
hausting the  air  over 
water  it  can  be  made 
to  boil  at  a  much 
lower  temperature. 
Whenever  the  ten- 
sion of  the  vapor 
equals  the  outside 
pressure,  boiling  be- 
gins. 

Experiment  I37-— 
Boil  some  water  in  a 
flask,  and  remove  the 

lamp.  "When  the  boiling  has  ceased,  cork  the  flask,  invert  it,  and 
pour  some  cold  water  on  its  base.  The  boiling  will  begin  again. 
The  cold  water  condensed  the  vapor  and  reduced  the  pressure. 


FIG.  236. — BOILING  AS  AN  EFFECT  OF  REDUCED 
PRESSURE. 


HEAT.  229 


This  principle  is  used  in  the  manufacture  of  certain  dye- 
stuffs,  and  in  sugar-refining,  where  it  is  desirable  to  evapo- 
rate the  water  at  a  low  temperature.  A  partial  vacuum  is 
formed  in  the  boiler,  and  the  steam,  as  fast  as  it  passes  off, 
is  condensed  by  a  falling  spray  of  water. 

As  we  ascend  a  mountain  the  boiling-point  lowers.  An 
approximation  to  the  height  may  be  formed  in  this  way : 
Eoughly,  the  height  in  feet  will  be  found  by  multiplying 
600  by  the  number  of  degrees  below  212°  F.  at  which 
water  boils. 

Questions. — 1.  On  a  certain  elevation  water  is  found  to  boil  at 
200°  F. :  what  is  its  height  ?  12  X  600  =  7200  feet,  nearly. 

2.  A  mass  of  gas  at  60°  C.  arid  under  a  pressure  of  30  inches 
measures  100  cubic  inches :  what  will  be  its  volume  at  40°  C.  and 
under  a  pressure  of  28  inches? 

Solution.—  At  60°  its  volume  will  be  -ffe  greater  than  at  0°  ;  at 
40°,  ¥Ys  greater.  Now,  100  cubic  inches  —  l^-,  or  fff,  its  volume 
at  0°.  Hence 

Volume  at  0°  =  ||f  X  100  =  81.9. 

Volume  at  40°  =  f  }f  of  81.9  ==  93.8. 

This  is  the  volume  under  30  inches  pressure.     Under  28  inches,  by 
Mariotte's  law,  the  whole  will  be  f|  of  93.8  =  100.5  cubic  inches. 

3.  A  mass  of  gas  at  0°  C.  occupies  a  litre  :  what  will  be  its  volume 
at  546°  C.  under  the  same  pressure?     Ans.  3  litres. 

381.  Steam. — Steam  occupies  about  1700  times  as  much 
space  as  the  water  which  produces  it.     In  other  words,  a 
cubic  inch  of  water  will  make  about  a  cubic  foot  of  steam. 

382.  Distillation. — Condensation  is  the  reverse  of  evapo- 
ration.    It  takes  place  whenever  the  vapor  is  reduced  in 
temperature  below  the  boiling-point  of  the  liquid.     This  is 
what  causes  the  formation  of  dew,  clouds,  and  rain.1    Dis- 
tillation is  the  condensation  of  certain  portions  of  a  liquid 
which  separate  from  contained  solids,  or  pass  off  at  a  lower 
temperature  than  the  remainder.     In  this  way  water  can 
be  separated  from  the  impurities  which  it  contains,  and 
alcohol  from  the  water  with  which  it  is  mixed. 

The  instrument  by  which  this  is  effected  is  a  still.    A 

1This  subject  will  be  found  more  fully  treated  in  the  chapter  on 
meteorology. 

20 


230 


NATURAL   PHILOSOPHY. 


retort  containing  the  liquid  is  heated  and  the  vapor  passed 
over  into  a  "  worm,"  which  is  kept  cool  by  being  immersed 


FIG.  237.— STILL. 

in  cold  water.  Here  the  vapor  is  condensed  and  runs  out 
at  the  lower  end,  while  the  solid  impurities  or  the  less 
volatile  liquids  remain  in  the  retort. 

Experiment  138. — Drop  a  little  water  on  a  piece  of  iron  heated  to 
about  150°  C.  It  will  form  into  a  drop  and  dance  about  the  surface, 
and  not  evaporate  very  rapidly.  Allow  the  plate  to  cool.  At  a  cer- 
tain temperature  the  drop  will  break,  spread  over  the  iron,  and 
almost  immediately  change  to  vapor. 

In  this  case  the  great  heat  of  the  plate  causes  such  a 
down-rush  of  steam  that  the  drop  rests  on  a  cushion  of  steam, 
and  not  on  the  plate.  This  fact  can  be  readily  seen  by 

Experiment  139. — Place  a  candle  in  the  right  position,  and  you 
can  see  light  between  the  drop  and  the  plate. 

TRANSMISSION   OF   HEAT. 

383.  Transmission  of  Heat. — Heat  travels  through  ether 
just  as  light  does.  The  vibrations  of  the  heated  body  are 
communicated  to  the  particles  of  ether  in  contact  with 
them,  these  act  on  the  next,  and  so  the  motion  is  extended. 
The  heat-  and  the  light-rays  are,  partly  at  least,  exactly 
the  same  rays.  Some  rays  give  us  sensations  of  both  light 


HEAT. 


231 


and  heat,  some  of  heat  only ;  hence  heat-  and  light-rays, 
being  largely  the  same,  follow  the  same  laws.  Heat,  like 
light,  decreases  as  the  square  of  the  distance  increases 


FIG.  238.— REFRACTION  OF  HEAT  BY  A  BURNING-GLASS. 

(see  Par.  257)  ;  it  is  refracted  in  accordance  with  the  "  law 
of  sines"  (see  Par.  280),  and  it  is  reflected,  making  the  angle 
of  incidence  equal  to  the  angle  of  reflection. 

384.  Luminous  and  Dark  Heat. — The  laws  are  the  same 
whether  the  heat  comes  from  a  glowing  body,  like  a  candle 
or  the  sun,  or  from  a  dark  body,  as  a  vessel  filled  with  hot 
water.     In  the  one  case  we  have  luminous  heat,  and  in  the 
other  we  have  dark  heat. 

385.  Radiation  and  Radiant  Heat. — The  passage  of  heat 
from  a  heated  body  is 

called  radiation,  and 
heat  on  its  passage  is 
radiant  heat. 

386.  Reflection    of 

Heat. — To  prove  that  FIG.  239.— REFLECTION  OF  HEAT. 

dark  heat  undergoes  reflection,  we  can  place  a  vessel  of 
boiling  water  at  the  principal  focus  (see  Par.  270)  of  a  con- 


232  NATURAL   PHILOSOPHY. 

cave  mirror,  when  the  heat-rays  will  be  reflected ;  and  if 
collected  by  another  concave  mirror,  a  thermometer  placed 
at  its  principal  focus  will  show  a  decided  increase  of  tem- 
perature. 

If  a  piece  of  ice  is  used  instead  of  the  vessel  of  hot 
water,  the  mercury  falls.  This  would  seem  to  indicate 
that  cold  is  also  reflected.  Such  is  not  the  case.  The 
cause  of  the  fall  is  that  the  thermometer  parts  with  its 
heat  faster  than  the  ice  does,  and  it  goes  to  the  ice  to  raise 
its  temperature,  or  to  melt  it. 

To  prove  the  refraction  of  heat  we  have  the  ordinary 
"  burning-glass." 

387.  Heat  Reflected,  Diffused,  Absorbed,  and  Transmitted, 
— Like  light,  all  the  heat  which  falls  on  a  body  is  not  re- 
flected.    Some  of  it  is  diffused  (scattered  in  all  directions), 
some  of  it  goes  into  the  body,  and  is  either  used  up  in 
doing  work  among  the  molecules  or  is  transmitted. 

388.  Different  Bodies  have  Different  Effects.— Different 
bodies  differ  greatly  in  their  power  of  radiating,  of  trans- 
mitting, of  reflecting,  and  of  absorbing  heat. 

389.  Difference  in  Radiation. — If  there  be  three  vessels 
of  equal  size  filled  with  hot  water,  one  made  of  polished 
tin,  one  coated  with  isinglass  and  one  with  lamp-black,  then 
in  the  same  time  there  will  be  eight  times  as  much  heat 
radiated  by  the  lamp-black  as  by  the  tin,  and  seven  times  as 
much  from  the  isinglass  as  from  the  tin.     As  a  general 
rule,  metallic  bodies  are  poor  radiators,  and  the  brighter 
and  smoother  the  surface  the  poorer  radiators  they  become. 
Good  reflectors  are  commonly  poor  radiators,  and  the  re- 
verse.    A  body  that  radiates  well  will  absorb  well  and  re- 
flect badly. 

390.  Difference  in  Transmission.— As  regards  transmis- 
sion of  heat,  certain  substances  which  are  opaque  to  light 
allow  heat  to  pass  freely,  and  some  transparent  to  light 
entirely   cut  off  the  heat.      In  the  chapter  on  light  we 
learned  that  blue  glass  allowed  blue  rays  to  pass  through 


HEAT.  233 

and  cut  off  the  red  :  in  the  same  way  thin  metallic  foil 
will  allow  luminous  rays  to  pass  and  cut  off  almost  all  the 
dark  heat.  Bad  radiators  are  bad  transmitters,  for  the 
bad  radiators,  like  polished  tin,  reflect  much  of  the  heat 
that  falls  on  them,  and  so  transmit  but  little. 

391.  Special  Substances. — Lamp-black   (the  soot   from 
lamps)  is  an  excellent  absorber ;  it  transmits  no  heat  and 
reflects  but  little.     Polished  silver  is  a  good  reflector;  it 
transmits  nothing  and  absorbs  very  little.     Eock-salt  in 
transparent  crystals  transmits  nearly  everything;  it  ab- 
sorbs none  and  reflects  but  little.     Crystals  of  alum,  equally 
transparent,  will  absorb  nearly  all  the  heat  and  transmit 
almost  none.     Ice  is  also  a  very  poor  transmitter. 

392.  Dr.  Franklin's  Experiment. — Dr.  Franklin  made  the 
experiment  of  putting  pieces  of  cloth  of  different  colors  on 
snow  when  the  sun  was  shining.     He  found  that  the  dark 
colors  melted  themselves  into  the  snow  farther  than  the 
light,  from  which  he  inferred  that  they  were  in  general 
better  absorbers.     This  is  true  in  so  far  as  it  relates  to 
luminous  heat,  but  in  the  case  of  dark  heat,  such  as  we  get 
from  a  stove,  color  does  not  seem  to  make  any  difference. 

393.  Effect  of  Screens. — A  screen  placed  in  front  of  a 
fire  protects  from  heat.     But,  as  it  receives  heat  itself,  it 
becomes  in  time  a  source  of  radiation.     We  do  not  feel  the 
radiation  so  strongly,  because  the  heat  which  it  intercepts 
it  sends  out  in  all  directions,  and  hence  not  so  strongly  in 
any  one. 

Exercises. — 1.  Should  stoves  be  kept  bright  if  we  desire  to  have 
the  most  heat  from  them?  Should  teapots  be  of  polished  metal? 
cylinders  of  steam-engines? 

2.  Which  is  cooler  in  the  direct  rays  of  the  sun,  light  clothing  or 
dark  ?  in  a  house  by  a  hot  stove  ? 

3.  If  we  had  a  convex  lens  of  alum  and  one  of  rock-salt  exposed 
to  the  sun,  in  the  focus  of  which  would  be  the  higher  temperature  ? 

4.  How  much  is  the  heat  diminished  by  moving  twice  as  far  from 
its  source  ? 

5.  The  dark  heat-rays  are  found  near  the  red  end  of  the  spectrum  : 
which  have  the  more  rapid  vibration,  the  dark  or  the  luminous  waves  ? 

6.  Is  a  glass  screen  as  effective  in  front  of  an  open  fire  as  in  front 
of  a  stove  ? 

20* 


234 


NATURAL   PHILOSOPHY. 


CONDUCTION   OF   HEAT. 

394.  Conduction  of  Heat. — When  heat  travels  along  by 
communicating  motion  from  one  particle  of  a  body  to  an- 
other, the  movement  is  called  conduction  of  heat.  Eadiation 
is  movement  through  ether,  and  radiant  heat  has  the  same 
velocity  as  light.  Conduction  is  a  comparatively  slow 
process. 

Experiment  140. — Heat  one  end  of  an  iron  rod  to  which  nails 
are  stuck  by  little  pieces  of  wax.  The  nails  will  drop  off  one  by  one 
as  sufficient  heat  reaches  them  to  melt  the  wax. 


FIG.  240. — CONDUCTION  OF  HEAT. 

395.  Different  Conducting  Power. — Diiferent  bodies  diifer 
in  their  power  to  conduct  heat. 

Experiment  141. — Hold  an  iron  rod  in  the  fire  till  it  begins  to  feel 
hot.  Hold  a  glass  rod  the  same  time,  no  perceptible  increase  of 
heat  is  felt. 

Experiment  142. — Coat  bars  of  various  substances  with  wax,  and 
place  them  all  with  one  end  in  hot  water.  Notice  how  far  on  each 
the  wax  melts. 


FIG.  241  .—DIFFERENT  CONDUCTING  POWER. 


396.  Conducting  Power  of  Metals. — The  following  table 
gives  the  relative  conducting  power  of  certain  metals : 


HEAT. 


235 


Silver 100 

Copper 74 

Gold 53 

Tin....  15 


Iron 12 

Lead 9 

Bismuth 2 


397.  Conducting  Power  of  Liquids  and  Gases. — Liquids 
and  gases  are  poor  con- 
ductors of  heat. 

Experiment  143. — Pack 
snow  in  a  test-tube,  and 
apply  heat  near  the  top. 
The  water  may  be  made  to 
boil  at  the  top  while  the 
snow  is  still  unmelted  at 
the  bottom. 

398.  Conducting 
Power    of    Air.— Dry 
air    is     a    poor     con- 
ductor of  dark  heat,  a 
better  one  of  luminous 
heat,  but  moist  air  is 
a  worse    conductor  of 
both  dark  and  luminous 
heat.     The  sun's  heat 
comes   to   us    through 
the  air  and  heats  up 
the   earth.     This  then 
radiates  dark  heat,  part 

of  which  is  retained  by  the  moist  air  surrounding  it. 

On  high  mountains  the  sun's  luminous  heat  penetrates 
the  rare  air  without  warming  it,  and  heats  the  mountain- 
tops.  But  the  radiated  heat  from  the.m  is  not  retained,  but 
quickly  passes  off,  leaving  the  air  cold.  A  cloud  or  fog 
over  the  mountain  would  change  all  this. 

The  glass  of  a  hot-house  produces  the  same  effect  as  the 
moisture  of  the  atmosphere. 

An  open  fire  gives  out  luminous  heat,  which  penetrates 
the  air  of  a  room  readily  and  warms  up  the  surfaces  of 
solid  bodies.  The  heat  from  a  stove  or  a  furnace,  on  the 


Fia.  242. — POOR  CONDUCTING  POWER  OP  WATER. 


236  NATURAL   PHILOSOPHY. 


contrary,  is  more  retained  in  the  air.  In  the  one  case  we 
keep  warm  by  direct  radiation,  in  the  other  by  living  in  a 
warm  atmosphere. 

Clothing  is  especially  useful  in  retaining  a  layer  of  warm 
air  next  the  body.  This  by  its  poor  conducting  power 
prevents  the  passage  of  heat  outward. 

399.  Sensation  of  Heat. — Our  sensation  of  heat  depends 
largely  on  the  conducting  power  of  the  substance  with 
which  we  are  in  contact.    A  carpet  and  an  oil-cloth  lying 
side  by  side  may  actually  contain  the  same  amount  of  heat. 
But  if  we  touch  both  at  the  same  time,  the  best  conductor, 
the  oil-cloth,  conducts  away  from  us  the  most  heat,  and  so 
seems  colder.     It  would  produce  the  same  effect  in  a  ther- 
mometer, carrying  away  heat  from  the  mercury. 

Exercises. — 1.  Why  is  a  glass  tumbler  more  readily  cracked  by 
hot  water  than  a  vessel  of  better  conducting  power? 

2.  Why  are  the  handles  of  teapots  often  made  of  glass  or  porcelain  ? 

3.  Why  is  woollen  clothing  warmer  than  cotton  ? 

4.  Why  can  a  man  plunge  his  hand  into  molten  iron  without  being 
burned  ? 

5.  A  brass  cylinder  covered  with  thin  paper  may  be  held  in  a 
flame  for  some  time  without  having  the  paper  scorched  ;  not  so  when 
the  cylinder  is  made  of  wood :  why  is  this  difference  ? 

6.  Why  do  hollow  walls  and  double  windows  keep  a  house  warm? 

7.  Would  a  hot-house  be  effective  if  heated  by  a  stove  from  above 
instead  of  by  the  sun? 

8.  Why  does  the  coming  of  clouds  frequently  make  it  warmer  ? 

9.  Are  our  sensations  safe  judges  of  temperature  ?     Having  had 
one  hand  in  ice  and  the  other  in  hot  water,  what  will  be  the  effect  if 
we  plunge  both  into  tepid  water  ? 

CONVECTION   OF   HEAT. 

400.  Convection  of  Heat. — When  a  liquid  or  a  gas  is  heated 
from  below,  the  warm  particles  rise  and  are  replaced  by 
colder  heavier   ones.      This   makes   constant   circulation, 
which  carries  the  heat  about.     This  method  of  conveying 
heat  by  actual  transmission  of  the  particles  of  water  is 
called  convection  of  heat. 

This  can  be  well  observed  in  the  boiling  of  water,  as 
seen  in  Experiment  136. 


HEAT.  237 


The  diffusion  of  heat  by  currents  is  shown  on  a  large 
scale  in  the  Gulf  Stream.  This  great  body  of  warm  water, 
which  is  a  result  of  the  heating  of  the  earth  at  the  equator, 
conveys  this  heat  to  the  coasts  of  England  and  Norway. 

THE   STEAM-ENGINE. 

401.  History  of  the  Steam-Engine, — About  the  year  1700 
a  machine  to  pump  water  out  of  mines  by  the  aid  of  steam 
was  invented  and  used  in  England,  but  about  1775  James 
Watt,1  a  Scotch  mathematical  instrument-maker,  invented, 
and  soon  after  brought  almost  to  its  present  perfection,  the 
stationary  engine.     The  first  locomotive-engine  was  built 
and  run  in  1804  or  1805  in  England.     But  it  was  not  until 
1829  that  the  first  really  efficient  locomotive  was  built  by 
George  Stephenson,1  an  Englishman. 

402.  The  Stationary  Engine. — Fig.  243  shows  the  essential 
features  of  the  stationary  engine.     M  is  the  boiler,  where 
the  steam  is  generated.     At  first  we  will  suppose  the  valve 
b  to  be  shut  and  a  to  be  open.     The  steam  will  pass  from 
the  boiler  through  a  and  drive  the  piston,  p,  to  the  bottom 
of  the  cylinder,     a  is  now  closed  and  b  and  d  are  opened. 
While  the  steam  is  now  passing  through  b  to  the  under 
side  of  the  piston  and  pushing  it  up,  that  steam  which  was 
above  the  piston  is  rushing  through  d  down  to  the  con- 
denser, I,  where  it  is  condensed  by  the  cold  water  there, 
leaving  a  vacuum  above  the  piston,  so  that  there  is  no 
obstacle  to  its  ascent.    When  it  reaches  the  top  of  the  cyl- 
inder again,  b  and  d  are  closed  and  a  and  c  opened,  and  so 
on  constantly.     The  figure  shows  how  the  up-and-down 
motion  of  the  piston  turns  the  fly-wheel,  E,  and  thence  by 
a  belt  or  otherwise  the  machinery  is  set  in  motion. 

1  Watt  and  Stephenson  were  two  of  the  greatest  benefactors  to 
mankind  that  ever  lived.  Samuel  Smiles  has  written  lives  of  both 
these  men  that  would  be  exceedingly  interesting  and  valuable  to 
every  one  who  studies  this  book. 


238 


NATURAL   PHILOSOPHY. 


403.  The  High-Pressure  Engine. — The  condenser  adds 
much  machinery  to  the  engine,  and  requires  a  constant 
supply  of  cold  water.  Many  engines,  therefore,  have  no 
condenser;  d  and  c  open  directly  into  the  air.  The  air 
condenses  the  steam  and  itself  fills  up  the  vacuum,  so  that 
the  piston  in  returning  has  to  drive  the  air  out  of  the 
cylinder  ahead  of  it.  With  a  condenser  the  piston  is  driven 
back  through  a  vacuum,  so  that  there  is  no  resistance ; 
without  it  the  piston  must  be  driven  against  the  pressure 
of  the  atmosphere,  nearly  15  pounds  per  square  inch. 


FIG.  243.— STATIONARY  ENGINE  (LOW-PRESSURE). 

When  there  is  no  condenser,  the  pressure  of  the  steam  must 
be  about  15  pounds  per  square  inch  greater  or  higher  to 
do  the  same  work :  hence  an  engine  without  a  condenser  is 
called  a  high-pressure  engine,  while  one  having  a  condenser 
is  called  a  low-pressure  engine.  Almost  all  small  stationary 
engines  are  high-pressure.  This  is  especially  true  of  por- 
table engines,  such  as  steam  fire-engines,  engines  for  work- 


HEAT. 


ing  thrashing-machines,  portable  saw-mills,  and  the  like. 
A  high-pressure  engine  of  course  takes  more  fuel  to  do  the 
same  work.  In  a  high-pressure  engine  the  steam  escapes 
from  the  cylinder  in  puffs,  and  this  puffing  is  characteristic 
of  this  kind  of  engine. 

404.  How  the  Valves  are  worked. — In  Fig.  243,  for  the 
sake  of  simplicity,  it  is  supposed  that  the  four  valves  are 
worked  by  hand.     Fig.  244  shows  how  one  valve  does  the 
work  of  all  four.     In  the  right-hand  figure  the  valve  is 
raised,  which  allows  the  steam  coming  in  by  the  pipe  on  the 
left  to  flow  into  the  lower  part  of  the  cylinder,  while  the 
peculiarly-shaped  valve,  called  a  D-valve,  connects  the  pipe 
from  the  other  end  of  the  cylinder  with  the  opening  0,  which 
leads  into  the  condenser.     When  the  piston  reaches  the 
upper  end  of  the  cylinder,  an  arm,  worked  by  the  engine 
itself,  pushes  the  D-valve  down,  as  seen  on  the  left,  and  the 
upper  part  of  the  cylinder  is  connected  with  the  boiler, 
while  the  lower  part  is  connected  with  the  condenser. 

405.  Three  Important  Attachments   to  the   Engine.— An 

opening  is  made  in  the  top  of  the  boiler,  which  is  closed  by  a  close- 


Fia.  244.— D-VALVE  AND  CYLINDER. 


FIG.  245. — THE  GOVERNOR. 


fitting  plug  of  iron.     This  plug  is  held  down  by  a  lever-arm,  at  the 
end  of  which  is  a  certain  weight.     When  the  pressure  of  the  steam 


240  NATURAL   PHILOSOPHY. 

becomes  so  great  that  there  is  danger  of  its  bursting  the  boiler,  it 
lifts  this  plug  and  escapes.  This  is  called  the  safety-valve.  A  gauge 
is  usually  attached  to  boilers,  which  shows  how  great  the  pressure 
upon  each  square  inch  is  at  any  time. 

Fig.  245  shows  a  very  ingenious  invention  of  Watt's,  which  auto- 
matically controls  or  governs  the  speed  of  the  engine  ;  hence  it  is 
called  the  governor.  This  is  so  attached  to  the  engine  that  it  re- 
volves. If  the  engine  runs  too  fast,  the  governor  will  revolve  faster, 
and  the  two  large  balls  will  be  thrown  outward  by  centrifugal  force. 
This  raises  R,  which  works  a  valve  and  shuts  off  a  part  of  the  supply 
of  steam  from  the  cylinder.  If  the  engine  runs  too  slow,  there  is  less 
centrifugal  force,  and  the  balls  fall,  which  lets  more  steam  into  the 
cylinder. 

The  large  wheel  seen  in  Fig.  243  is  the  fly-wheel.  It  is  a  heavy 
iron  wheel,  and,  besides  running  the  belt  which  drives  the  machinery, 
it  is  of  great  use  in  equalizing  the  motions  of  the  engine  and  in 
storing  up  power  so  as  to  overcome  by  its  inertia  sudden  resistances 
to  the  machinery. 

406.  The  Locomotive. — Fig.  246  is  a  section  of  a  loco- 
motive, showing  its  essential  parts.  In  order  to  reach  the 
smoke-stack  the  heated  air  and  flames  of  the  fire  must 
pass  through  metal  tubes.  These  tubes  run  directly 
through  the  boiler,  and  are  very  numerous,  thus  giving  a 
very  large  heating  surface.  They  are  surrounded  by  the 
water  in  the  boiler,  and  without  these  tubes  it  would  be 
impossible  to  make  steam  fast  enough  to  drive  the  loco- 
motive at  high  speed.  The  cylinder  is  seen  in  front,  and 
right  above  it  is  the  D-valve,  worked  by  the  small  rod 
which  may  be  seen  connecting  it  with  the  other  machinery. 
The  locomotive  has  no  condenser,  and  is  therefore  a  high- 
pressure  engine.  The  steam  escapes  from  the  cylinder 
through  the  D-valve  into  the  blast-pipe  v,  and  thence  up  the 
smoke-stack.  This  greatly  increases  the  draught  of  the  fire, 
and  causes  the  puffs  of  sound  that  we  hear,  and  the  puffs 
of  smoke  that  we  see.  Increasing  the  draught  by  letting  the 
waste  steam  escape  through  the  chimney,  like  the  tubes  in 
the  boiler,  was  a  very  important  invention,  as  it  keeps  up 
a  hotter  fire  and  thus  generates  steam  faster. 


HEAT. 


241 


Every  one  who  uses  this  book  is  strongly  urged  to  examine  thor- 
oughly engines  of  both  sorts.  Engineers  will  generally  be  willing  to 
explain  all  their  details. 


FIG.  246.— THE  LOCOMOTIVE  ENGINE  (HIGH-PRESSURE). 

407.  How  the  Power  of  the  Steam-Engine  is  estimated. — 
The  power  of  an  engine  is  usually  estimated  in  horse-power. 
Watt  estimated  that  a  horse  could  raise  1000  tons  one  foot 
high  in  an  hour.1  An  engine  that  can  do  that  much  work 
is  a  one  horse-power  engine ;  one  that  can  lift  5000  tons  one 
foot  in  an  hour,  or  its  equivalent,  is  a  five  horse-power  en- 
gine. It  is  found  that  the  steam  produced  from  one  cubic 

1  The  raising  of  one  ton  1000  feet  in  an  hour,  of  half  a  ton  2000 
feet  in  the  same  time,  or  any  other  equivalent,  would  be  one  horse- 
power. 

L  21 


242  NATURAL  PHILOSOPHY. 


foot  of  water  will  just  about  raise  1000  tons  one  foot  per 
hour,  so  that  an  engine  which  can  change  five  cubic  feet  of 
water  into  steam  each  hour  is  a  five  horse-power  engine. 

The  student  will  not  fail  to  notice  that  the  steam-engine 
is  a  notable  example  of  the  conversion  of  energy.  Heat  is 
changed  to  mechanical  force  by  the  agency  of  steam  and 
the  machinery  of  the  engine.  Neither  the  steam  nor  the 
engine  produces  the  power,  and  in  the  most  efficient  engine 
they  really  waste  a  great  deal  of  it.  But  they  are  the 
best  means  yet  found  of  converting  the  molecular  motion 
or  force  of  the  heat  into  mechanical  motion.  Nor  will 
it  be  forgotten  that  the  power  to  produce  heat  is  in  the 
coal,  and  was  stored  away  by  the  sun's  light  and  heat  ages 
ago  in  the  forests  which  produced  our  coal-beds.  So  it  is 
really  the  sun's  light  and  heat  shed  upon  the  earth  many 
thousands  of  years  ago  that  are  drawing  all  our  railway- 
trains,  driving  all  our  steamships,  and  moving  all  our  steam 
machinery  to-day. 

General  Exercises. — 1.  Find  the  degree  in  the  Centigrade  scale 
which  corresponds  to  113°  F.,  and  that 'which  corresponds  to  140°  F. 

2.  Find  the  degree  in  Fahrenheit's  scale  which  corresponds  to  15° 
C.,  and  that  which  corresponds  to  35°  C. 

3.  A  piano  which  has  been  tuned  in  a  drawing-room  in  a  morning 
may  produce  discords  in  the  evening,  when  the  room  is  heated  by  the 
pressure  of  a  large  evening  party  :  explain  this. 

4.  A  flask  with  a  long  neck  contains  alcohol,  which  fills  the  flask 
and  rises  to  some  height  in  the  neck  ;  the  flask  is  placed  in  hot  water, 
and  the  liquid  at  first  falls  in  the  neck  as  if  it  were  contracting  :  ex- 
plain this. 

5.  Show  that  30  cubic  inches  of  air  would  expand  to  about  41  in 
passing  from  0°  C.  to  100°  C. 

6.  A  gas  measures  98  cubic  inches  at  185°  F. :  find  what  it  will 
measure  at  10°  C.  under  the  same  pressure.     Ans.  77,  about. 

7.  If  50  cubic  inches  of  air  at  5°  C.  below  0°  C.  are  raised  to  15° 
C.  under  the  same  pressure,  find  the  volume.     Ans.  53.8,  about. 

8.  Air  which  is  known  to  have  a  volume  of  100  cubic  inches  at  0° 
C.  is  found  to  have  expanded  to  120  cubic  inches  without  any  change 
of  pressure :  determine  the  temperature.     Ans.  54.6°. 

9.  Find  what  weight  of  ice  at  0°  C.  will  be  melted  if  put  in  a 
pound  of  water  at  50°  C.     Ans.  10  ounces. 

10.  A  mixture  is  made  of  3  pounds  of   water  at  12°  C.  with  3 
pounds  of  water  at  16°  C.  :    find  the  temperature  of  the  mixture. 
Ans.  14°. 


HEAT.  243 


11.  A  mixture  is  made  of  4  pounds  of  water  at  7°  C.  with  6  pounds 
of  water  at  12°  C. :  find  the  temperature  of  the  mixture.     Ans.  10°. 

12.  Unglazed  pottery  is  sometimes  used  to  hold  water  and  to  keep 
it  cool :  explain  this. 

13.  Carbonic  acid  may  be  reduced  to  the  liquid   form  by  strong 
pressure  ;  when  the  pressure  is  removed,  the  liquid  returns  to  the  state 
of  gas,  but  some  of  it  becomes  solid  carbonic  acid  :  explain  this. 

14.  A  pound  of  iron  at  99°  C.  is  immersed  in  a  pound  of  water  at 
0°  C. :  find  how  many  degrees  the  temperature  of  the  water  will  be 
raised,  taking  the  specific  heat  of  iron  at  .1.     Ans.  9. 

15.  The  air  on  a  high  mountain   may  be  intensely  cold  although 
the  sun  is  shining  and  no  clouds  exist:  explain  this. 

16.  The  bulb  of  a  mercurial  thermometer  is  exposed  to  heat:  will 
any  difference  be  produced  in  the  rate  of  rising  of  the  mercury  if  the 
bulb  is  covered  with  silver  foil  ? 

17.  Suppose  we  are  provided  with  bars  of  copper,  silver,  gold,  and 
platinum  :  explain  how  we  must  proceed  to  determine  the  conductive 
power  of  these  metals. 

18.  A  piece  of  platinum  may  be  held  in  the  hand  while  one  end  is 
red-hot,  but  a  piece  of  copper  of  the  same  length  under  such  circum- 
stances will  speedily  burn  the  fingers  :  explain  this. 

19.  A  kettle  which  has  been  in  use  for  some  time  often  becomes 
coated  by  a  deposit  on  the  inside,  and  then  water  takes  a  long  time 
to  boil  in  it :  explain  this. 

20.  A  weight  of  a  ton  is  lifted  by  a  steam-engine  to  the  height  of 
386  feet :   find  how  many  units  of  heat  are  required  for  this  work. 
Ans.  1000. 

21.  A  68-pound  cannon-ball  strikes  a  target  with  a  velocity  of 
1544  feet  per  second  :  supposing  all  the  heat  generated  by  the  collision 
to  be  communicated  to  68  pounds  of  water,  how  many  degrees  would 
the  temperature  of  the  water  be  raised  ?     Ans.  2. 

22.  Show  that  to  raise  the  temperature  of  a  pound  of  iron  from  0° 
C.  to  100°  C.  an  amount  of  heat  is  required  which  would  lift  about 
3|  tons  of  iron  a  foot  high. 


244  NATURAL   PHILOSOPHY. 


CHAPTEE   VIIL 
MAGNETISM. 

408.  Magnets. — A  certain  ore  of  iron,1  frequently  called 
loadstone,  possesses  the  property  of  attracting  metallic  iron 
and  steel  quite  strongly,  and  of  attracting  many  other  sub- 
stances very  slightly.  A  piece  of  iron,  while  near  or  in 
contact  with  a  loadstone,  possesses  the  same  property,  and 
a  piece  of  steel  placed  in  contact  with  the  loadstone  not 
only  acquires  this  property,  but  retains  it  after  having  been 
withdrawn.  The  mountains  surrounding  the  ancient  city 
of  Magnesia,  in  Asia  Minor,  were  formerly  famous  for  the 
production  of  loadstone,  and  from  this  city  the  name  mag- 
net has  come  to  be  applied  to  a  piece  of  loadstone,  or  to  any 
piece  of  iron  or  steel  exhibiting  the  same  power  of  attrac- 
tion. When  we  have  finished  this  chapter  and  the  next,  we 
shall  have  learned  that  there  are  many  ways  of  imparting 
this  interesting  property  to  bars  of  iron  and  steel.  At  pres- 
ent we  will  consider  magnetism,  or  this  power  of  attraction, 
as  a  property  communicated  by  the  loadstone  or  "  natural 
magnet."  Good  loadstones  are  small,  inconvenient,  and  ex- 
pensive, and  bars  of  steel  which  have  been  stroked  from  end 
to  end  with  the  loadstone  become  magnets  themselves,  and 
are  capable  of  transmitting  the  power  to  others.  We  shall, 
therefore,  use  steel  magnets  for  our  present  experiments, 
and  learn  how  to  make  them  as  we  progress.  A  pair  of 
such  magnets,  from  three  to  six  inches  long,  may  be  had 

1  An  oxide  of  iron,  usually  of  the  composition  Fe304.  A  large 
proportion  of  this  ore  of  iron  does  not  exhibit  magnetic  properties. 


MAGNETISM. 


245 


for  a  small  sum,  and  will  answer  well  for  many  of  the  fol- 
lowing experiments. 

409.  Poles    Of    Magnets. — Experiment  "144.— Lay  a  magnet 
down  on  a  bed  of  iron-filings,  or  in  a  box-lid  containing  a  quantity 
of  carpet-tacks  or  finishing-nails  or  "  card-teeth."     Be  sure  they  are 
evenly  distributed,  so  that  all  parts  of  the  magnet  may  have  equal 
access  to  them.     Pick  up  the  magnet,  holding  it  horizontally  by  the 
middle.    Notice  that  the  small  particles  of  iron  are  clustered  at  the 
ends,  and  that  very  few  are  to  be  found  near  the  middle. 

The  attractive  power  of  magnets  resides  at  or  very  near 
the  ends.  These  are  termed  the  poles  of  the  magnet. 
Every  ordinary  magnet  has  two  poles. 

410.  The  Two  Poles  of  a  Magnet  different  in  Kind.— Ex- 
periment   145.— Touch  two 

magnets  together,  end  to  end, 
and  reverse  one  of  them  and 
then  the  other  several  times. 
Unless  they  are  very  different 
in  size  or  strength,  it  will  b« 
found  that  in  two  positions 
they  attract  and  adhere  to 
each  other,  and  in  the  remain- 
ing two  positions  they  do  not. 
Put  temporary  marks  on  the 
poles  (if  not  already  marked), 
so  that  they  may  be  dis- 
tinguished. 

Experiment  146. — B  a  1  - 
ance  one  of  the  magnets  on 
the  edge  of  a  ruler.  Bring 
each  end  of  the  other  magnet 
from  above  quite  near  to  each 
end  of  the  balanced  magnet. 
If  the  balancing  is  delicate 
enough,  it  will  be  found  that 
the  ends  which  in  the  pre- 
vious experiment  refused  to  attract  each  other,  actually  repel  each 
other. 

From  these  experiments  it  is  evident  that  the  two  poles 
of  a  magnet,  although  capable  of  producing  the  same  ap- 
parent effect  in  the  iron-filings  or  tacks,  are  in  some  way 
different. 

411.  Action  of  Similar  and  Dissimilar  Poles.— Experiment 

147. — Hold  two  magnets  of  the  same  size  and  strength  perpendicu- 
larly, one  in  each  hand,  and  dip  the  lower  end  of  each  into  a  pile  of 

21* 


FIG.  247.— ACTION  OF  SIMILAR  AND  DISSIMILAR 
POLES. 


246 


NATURAL   PHILOSOPHY. 


little  nails,  or  something  similar.  Now  bring  the  loaded  magnets 
together,  side  by  side.  Keverse  one  of  the  magnets,  and  repeat  the 
experiment.  In  one  case  the  loads  will  remain  adhering  to  the  mag- 
nets after  they  are  brought  together,  in  the  other  case  the  loads  will 
drop  as  soon  as  the  magnets  touch  each  other.  Notice  that  the  poles 
which  are  together  when  loads  are  sustained  are  those  which  were 
marked  as  repelling  each  other  in  Experiment  146,  while  those  which 
are  together  when  the  loads  are  dropped  are  those  which  were  marked 
as  attracting  each  other. 

It  is  evident  that  when  the  two  poles  unitedly  sustain 
the  double  load,  they  must  be  acting  together,  —  i.e.,  they  must 
be  similar,  —  and  that  when  the  two  poles  which  were 
strong  separately  refuse  to  hold  any  load  unitedly,  they 
must  be  acting  differently  or  'oppositely,  —  i.e.,  they  must  be 
dissimilar.  We  are  now  ready  to  mark  the  poles  of  our 
magnets  again,  but  not  permanently  yet.  Put  similar 
marks  upon  the  poles  that  act  together  in  sustaining  the 
double  load.  From  these  experiments  we  derive  the 

Law  of  Action  between  Magnets  : 

Similar  magnetic  poles  repel  each  other;  dissimilar  magnetic 
poles  attract  each  other. 

412.   Iron  magnetized  by  Induction,  —  Experiment  148.— 

With  either  pole  of  a  magnet  pick  up  a  nail  not  too  large  to  adhere 
firmly  to  the  magnet  and  to  stand  out  from  it  in  any  position.  Touch 
the  free  end  of  this  nail  to  another  nail  of  the  same  size  or  smaller. 

It  will  be  attracted.  If  the 
magnet  is  strong  enough, 
the  second  nail  will  support 
(suspend)  a  third,  this  a 
fourth,  and  so  on. 

Experiment  149.  —  Touch 
the  lower  end  of  the  chain 
of  nails  of  the  last  experi- 
ment with  that  pole  of  the 
other  magnet  which  is  dis- 
similar to  the  pole  from 
which  the  nails  are  hang- 
ing. It  will  adhere  firmly. 
Form  a  chain  again  on  a 
pole  of  one  magnet,  and  ap- 
proach its  lower  extremity 
with  the  similar  pole  of  the 
other  magnet.  The  nails 

will  either  be  repelled  or  else  they  will  let  go  their  hold  on  one  another 
and  drop.  If  there  are  several  nails  in  the  chain  they  will  probably  all 


FIG.  248.—  NAILS  MAGNETIZED  BY  INDUCTION, 


MAGNETISM.  247 


drop,  one  by  one,  till  the  last  one  is  reached,  and  it  will  be  strongly 
repelled.  Vary  the  experiment  as  follows :  Kest  the  upper  magnet 
on  a  table  top,  so  that  one  pole  will  project  beyond  the  edge  of  the 
table.  Attach  a  chain  of  nails  to  this  pole,  and,  when  the  magnet  is 
nearly  loaded,  carefully  pull  the  top  nail  downward  a  short  distance 
from  the  magnet  to  which  it  adheres.  If  this  is  done  carefully  the  nails 
will  still  adhere  to  one  another,  and  exhibit  the  same  properties  of  at- 
traction and  repulsion  that  they  did  while  the  upper  nail  was  in  con- 
tact with  the  magnet. 

This  experiment  shows  that  there  are  two  dissimilar  poles 
in  each  nail  while  it  is  near  to,  or  in  contact  with,  the  mag- 
net ;  in  fact,  that  each  nail  is  then  a  magnet  in  itself.  It 
is  the  steel  magnet  which,  by  its  presence,  induces  the  nails 
thus  to  act  as  magnets,  and  they  are  accordingly  said  to  be 
magnetized  by  induction.  Remember  this  word  and  the 
reason  for  its  use,  as  it  will  be  found  frequently  in  this  and 
the  following  chapter. 

413.  Magnetization  of  Steel.— Steel  is  magnetized  by  in- 
duction, as  iron  is,  but  it  is  very  much  slower  in  yielding  to 
the  magnet's  influence.     If  one  end  of  a  needle  be  placed 
against  a  pole  of  a  magnet  it  will  exhibit  very  little  at- 
traction at  its  farther  end.     It  requires  repeated  strokes 
across  the  end  of  a  magnet  fully  to  magnetize  it,  but  when 
once  magnetized,  the  steel,  if  good,  retains  its  magnetism. 

Experiment  150. — Lay  an  ordinary  needle  on  one  pole  of  a  magnet, 
and,  taking  it  by  either  end,  draw  it  slowly  across  the  magnet  until 
it  is  torn  loose  from  it.  Lay  it  on  the  other  pole  of  the  magnet,  take 
it  by  the  other  end,  and  draw  it  across  as  before.  Kepeat  this  a  few 
times,  being  careful  that  the  same  end  of  the  needle  shall  in  each 
case  be  pulled  from  the  same  end  of  the  magnet.  The  needle  will  be 
found  to  be  permanently  magnetic. 

414.  Large  Magnets. — Large  steel  magnets  may  be  made 
in  a  similar  manner,  except  that  the  bar  to  be  magnetized 
is  generally  laid  on  a  flat  table  and  one  or  two  good  mag- 
nets are  drawn  along  it  several  times.   The  magnets  which 
are  thus  used  do  not  lose  any  of  their  own  strength,  though 
they  impart  the  same  amount  to  any  number  of  bars.    As 
a  matter  of  fact,  large  steel  magnets  are  generally  made  by 
contact  with  powerful  electro-magnets.    Further  reference 


248  NATURAL  PHILOSOPHY. 

to  the  subject  must  therefore  be  left  till  we  reach  electro- 
magnetism. 

415.  Poles  in  the  Particles  of  a  Magnet,— Experiment  151.— 

Magnetize  two  sewing-needles  so  that  corresponding  ends  shall  be 
similar  poles,  and  test  the  strength  of  one  with  very  small  tacks.  Cut 
it  in  half,  and  lay  the  pieces  in  a  bed  of  the  tacks.  Each  half  will  be 
a  complete  magnet  with  two  poles.  Compare  the  poles  with  the  uncut 
needle.  They  will  be  found  to  correspond  in  kind  with  the  poles  to 
which  they  were  nearest  in  the  whole  needle.  Cut  either  half  again 
and  again,  until  the  pieces  are  very  small.  In  each  case  each  piece 
will  exhibit  two  poles,  and  each  pole  will  be  found  as  strong  as  the 
original  poles  of  the  whole  needle. 

We  may  make  any  number  of  short  magnets  by  cutting 
up  a  longer  one,  the  limit  being  reached  only  when  the 
pieces  become  so  small  that  we  can  no  longer  divide  them 
with  our  cutting-tools.  As  we  know  the  pieces  of  steel  to 
be  composed  of  infinitely  smaller  pieces  than  we  can  thus 
make,  we  may  fairly  conclude  that  each  particle  of  a  mag- 
net possesses  the  poles  and  other. essential  properties  of  the 
whole  magnet.  This  is  also  the  case  with  the  particles  of 
a  bar  of  iron  which  is  rendered  magnetic  by  the  inductive 
influence  of  a  magnet  near  it. 

416.  Why  a  Bar  is  magnetized, — We  are  now  ready  to 
state  a  little  more  clearly  the  theory  of  magnetism  as  ex- 
hibited in  iron  and  steel  bars.     For  the  purpose  of  illustra- 
tion, we  will  consider  a  bar  to  be  a  line  of  single  particles 
placed  end  to  end.    When  such  a  bar  is  brought  sufficiently 
near  the  pole  of  a  magnet,  the  particle  nearest  the  magnet 
is  polarized  by  induction  ;  that  is,  it  has  two  poles  formed 
in  it,  one  of  which  is  attracted  by  the  pole  of  the  magnet, 
and  the  other  repelled.     The  attracted  pole  is,  of  course, 
unlike  the  contiguous  pole  of  the  magnet,  and  the  repelled 
pole  is  like  it.     This  particle  then  acts  by  induction  on  the 
second  particle,  thus  polarizing  it;  this  acts  on  the  third, 
the  third  on  the  fourth,  and  so  on  until  all  the  particles  are 
polarized,  each  one  by  the  influence  of  the  one  next  to  it. 
When  the  particles  are  all  thus  polarized,  each  pole  is  en- 
gaged in  attracting  the  pole  next  to  it,  except  those  at  the 


MAGNETISM.  249 


two  extremities  of  the  bar.  These  two,  accordingly,  are  free 
to  polarize  and  attract  other  pieces  of  iron,  and  they  are 
therefore  the  poles  of  the  magnet. 

417.  Poles  may  be  neutralized. — If  the  two  poles  of  a 
magnet  be  allowed  to  exert  their  attraction  fully  on  each 
other,  the  magnet  loses  its  power  of  attracting  other  bodies. 
This  may  be  beautifully  shown  by  the  following : 

Experiment  152. — Procure  a  piece  of  watch-spring  about  six 
inches  long  (your  jeweller  will  willingly  contribute  it),  and  magnetize 
it  by  drawing  it  several  times  by  alternate  ends  between  the  thumb 
and  the  respective  poles  of  a  magnet.  Dip  the  poles  of  the  magnet 
thus  formed  into  small  tacks.  Carefully  lift  the  load,  and  bring  the 
poles  together  so  as  to  make  a  circle  of  the  spring.  The  load  will 
drop,  and  any  attempt  to  make  it  adhere  to  any  part  of  the  circle 
will  be  in  vain  if  the  spring  has  been  evenly  magnetized.  In  Ex- 
periment 147  the  same  effect  was  exhibited  with  the  unlike  poles  of 
two  magnets. 

418.  The  Attracted  Body  polarized. — Every  particle  of 
iron  or  steel  attracted  by  a  magnet  is  first  polarized  by  the  at- 
tracting magnet,  unless  previously  polarized  by  some  other 
means.     Fig.  249   suggests   an    experiment   for  verifying 


FIG.  249.— MAGNETIC  INDUCTION. 

this  law.  The  smaller  piece  is  soft  iron.  ("  Soft  iron"  is 
the  technical  name  for  good  wrought  iron,  and  is  used  in 
distinction  from  steel.)  If  the  piece  of  soft  iron  in  the 
above  figure  were  of  the  same  size  in  cross-section  as  the 
magnet,  and  the  two  were  placed  in  contact,  end  to  end, 
there  would  no  longer  be  any  poles  at  the  junction,  but 
there  would  be  one  at  each  end  of  the  compound  bar. 


250 


- 

DEI  *T  OF  PHYSICS 

NATURAL   PHILOSOPHY. 


419.  Compound  and  Horseshoe  Magnets.  —  As  the  at- 

tracted piece  of  iron  is  polarized,  it  is  evi- 
dent that  the  magnet  would  attract  each  end 
equally  if  it  could  reach  them  both  at  once. 
To  accomplish  this  end,  magnets  are  fre- 
quently bent  into  the  form  of  a  capital  U. 
Such  magnets  are  called  "  horseshoe"  mag- 
nets. The  action  of  a  horseshoe  magnet  on 
a  piece  of  soft  iron  is  indicated  in  Fig.  250. 
The  soft  iron  is  called  the  keeper.  When  so 
constructed  as  to  move  pieces  of  machinery, 
it  is  called  an  armature.  To  obtain  the  best 
results  from  a  large  magnet  of  any  shape,  it 
must  be  made  by  fastening  several  smaller 
bars  together,  parallel  with  one  another. 
FIG.  250.—  COMPOUND  This  makes  a  compound  magnet.  Fig.  250 

HORSESHOE    MAG-   . 

NET  AND  KEEPER,  is  a  compound  horseshoe  magnet. 

420.  Lines  of  Force.—  Experiment  153.—  Cut  a 

groove  in  the  face  of  a  smooth  board,  so  that  a  flat  bar  magnet  may  lie 


FIG.  251. — LINES  OF  MAGNETIC  FORCE. 


in  it  and  have  its  upper  side  flush  with  the  board.     Place  the  magnet 
in  the  groove,  cover  it  over  with  a  smooth  sheet  of  writing-paper,  and 


MAGNETISM.  251 


sift  iron-filings  l  well  over  the  paper.  The  position  of  the  magnet  is 
plainly  indicated  by  the  filings.  Tap  the  board  gently,  and  the 
filings  will  arrange  themselves  in  a  series  of  curves  as  shown  in  Fig. 
251. 

These  curves  are  called  the  lines  of  force  of  the  magnet. 
They  show  the  direction  which  any  other  magnet,  placed 
in  the  plane  of  the  paper,  and  influenced  by  the  covered 
magnet,  tends  to  assume.  The  following  beautiful  experi- 
ment shows  that  these  lines  of  force  exist  in  all  planes 
other  than  that  which  happens  to  be  occupied  by  the 
paper. 

Experiment  154. — Take  an  ordinary  whalebone,  or  a  similar  piece 
of  elastic  wood,  a  few  inches  long,  and  string  it  as  a  bent  bow,  with 
a  silk  thread  which  has  been  unspun  or  combed  out  so  that  it  will 
have  no  tendency  of  its  own  to  twist.  Tie  a  knot,  or  stick  a  piece  of 
wax,  in  the  middle  of  the  string.  Thrust  a  sharp  needle,  which  has 
been  magnetized,  half-way  through  the  knot  or  bunch  of  wax. 
Taking  hold  of  the  bow  for  a  handle,  approach  a  magnet  with  the 
needle.  Whether  the  needle  be  held  above,  below,  on  either  side,  or 
in  any  oblique  position  with  reference  to  the  magnet,  it  will  always 
assume  a  position  corresponding  to  the  direction  of  the  lines  of 
filings  in  the  preceding  experiment. 

421.  Intensity  of  Magnetic  Attraction. — "We  notice  in  Ex- 
periment 153  that  the  filings  near  the  pole  are  much  more 
powerfully  affected  than  those  farther  off.     The  needle  of 
Experiment  154  was  agitated  most  violently  when  near 
either  pole  of  the  magnet.     When  we  approach  the  pole 
of  a  magnet  with  a  piece  of  iron,  we  notice  how  the  attrac- 
tion seems  to  strengthen  as  the  distance  between  them  be- 
comes less.     With  delicate   appliances  for  measuring  the 
pull  or  push  exerted  by  magnets  on  other  bodies,  or  on 
each  other,  we  learn  the 

Law  of  Magnetic  Attraction : 

Magnetic  attraction  or  repulsion  varies  inversely  as  the  square 
of  the  distance  through  which  it  acts. 

Notice  that  the  laws  of  gravitation,  sound,  light,  heat,  etc.,  acting 
through  different  distances,  are  similar  to  this. 

422.  Directive  Tendency  of  the  Magnet. — Experiment  155. 

— Make  a  stirrup  of  paper,  and  hang  it  to  a  convenient  support  by  a 
1  Iron-filings  may  be  bought  of  a  dealer  in  chemicals. 


252' 


NATURAL   PHILOSOPHY. 


string  that  has  no  tendency  to  twist.  Balance  in  the  stirrup,  one  at 
a  time,  the  two  magnets  which  have  been  used  in  many  of  the  previ- 
ous experiments.  After  swinging  backward  and  forward  a  few  times, 
the  magnets  will  each  come  to  rest,  pointing  nearly  north  and  south. 
It  will  be  found  that  the  ends  of  the  two  magnets  which  point  in 
either  of  these  directions  are  those  which  were  marked  as  similar  to 
each  other  after  we  had  tried  Experiment  147.  "We  are  now  ready  to 
mark  the  poles  of  our  magnets  permanently.  Mark  the  pole  which 
points  northward  "N,"  for  north,  or, rather,  north-pointing,  and  mark 
the  other  end  "6',"  for  south-pointing. 

All  magnets  tend  to  arrange  themselves  in  nearly  a  north- 
and-south  direction.  This  is  because  of  magnetic  property 
in  the  earth  itself.  Indeed,  the  whole  earth  may  be  con- 
sidered  as  a  vast  magnet,  having  its  magnetic  poles  near 
the  geographical  poles.  How  the  magnetism  of  the  earth 
is  supposed  to  originate  will  be  referred  to  in  a  subsequent 
chapter. 

423.  The  Magnetic  Needle. — A  thin  magnet,  nicely  bal- 
anced on  a  hard  point,  so  that  it  may  have  great  freedom 
of  motion,  is  called  a  magnetic  needle.  Fig.  252  shows  a 
common  form. 


FIG.  252.— MAGNETIC  NEEDLE. 


FIG.  253.— HOME-MADE 
NEEDLE. 


Experiment  156. — To  make  a  very  good  magnetic  needle,  take  a 
piece  of  watch-spring  six  or  eight  inches  long.     Straighten  it  between 


MAGNETISM.  253 


the  thumb  and  finger.  Then,  holding  the  middle  of  it  in  the  flame 
of  a  lamp,  bend  it  as  nearly  "double"  as  possible  without  breaking. 
Bend  the  ends  back  into  a  line  with  each  other,  as  shown  in  Fig.  253. 
Magnetize  each  end  separately.  Wind  a  waxed  thread  around  the 
short  bend  that  is  left,  and  balance  on  a  needle  held  upright  in  a  flat 
cork  or  a  card.  A  little  filing  or  grinding  will  be  necessary  to  make 
it  balance.  With  a  point  filed  on  the  north-pointing  pole  the  needle 
is  finished. 

424.  The  Compass. — A  magnetic  needle,  when  fixed  in  a 
frame  which  is  graduated  in  degrees  and  properly  equipped 
with  sights   and    levels,   forms   the   surveyor's    compass. 
When  the  needle  carries  a  circular  card  with  the  "  points" 
(north,  south,  east,  west,  etc.)  marked  on  it,  the  arrange- 
ment is  the  essential  feature  of  the  mariner's  compass. 

425.  Magnetic  Declination. — Although  the  compass  was 
used  a  thousand  years  before  the  Christian  era,  it  has  long 
been  known  that  in  most  places  the  direction  of  the  needle 
is  not  a  true  north-and-south  line.    The  deviation  from  the 
meridian  is  called  the  declination  of  the  compass.   Navigators 
must  know  the  declination  for  a  given  place  and  allow  for 
it.     If  the  declination  in  a  given  place  were  constant,  the 
allowance  could  easily  be  made,  but  it  is  subject  to  many 
variations,  some  extending  over  long  periods,  some  over 
shorter  periods,  some  regular  and  some  irregular.     As  the 
greatest  amounts  of  variation  occur   regularly  and  take 
place  slowly,  the  compass  is  still  a  valuable  aid  to  navi- 
gators and  explorers.     The  declination  at  Philadelphia  in 
1883  is  about  5°  west.     At  London  it  is  about  20°  west. 

426.  Magnetic  Dip. — If  a  steel  bar  be  exactly  balanced 
in  its  centre  of  gravity  so  that  it  may  move  about  its  sup- 
port in  any  direction,  and  then  magnetized,  it  will  not  re- 
main level,  but  (in  the  Northern  hemisphere)  the  north- 
pointing  pole  will  incline  downward,  pointing  towards  a 
place  considerably  below  the  horizon.     This  is  known  as 
the  dip  of  the  needle,  and  a  needle  so  balanced  and  mag- 
netized is  a  dipping  needle.     The  dip  is  greater  the  nearer 
we  approach  to  the  magnetic  poles  of  the  earth.     In  the 
Southern  hemisphere  the  south-pointing  pole  dips  down, 

22 


254 


NATURAL  PHILOSOPHY. 


The  dipping  needle  indicates  the  direction  of  the  earth's 
lines  of  magnetic  force.  Therefore,  if  we  know  the  position 

of  the  magnetic  poles 
of  the  earth,  latitude 
may  be  roughly  deter- 
mined by  means  of  a 
dipping  needle.  Hum- 
boldt1  relates  that  on 
one  occasion  he  suc- 
cessfully directed  his 
vessel  into  the  port  of 
Callao,  on  the  west 
coast  of  South  Amer- 
ica, by  determining  his 
latitude  in  this  way. 

The  dip  of  the  needle 
at  Philadelphia  is  about 
^____  75°  with  the   horizon. 

FIG.  254.— NEEDLE  INDICATING  BOTH  DIRECTION      The  magnetic  equator, 

AND  DtP.  ,.  f  ^• 

or   line   of  no   dip,   is 

somewhat  irregular  in  shape,  but  crosses  the  equator  in 
two  points  at  an  angle  of  about  12°,  being  that  distance 
north  of  the  equator  in  the  Indian  Ocean  and  the  same 
distance  south  in  Brazil.  The  north  magnetic  pole  is  about 
10°  north  of  the  north  shore  of  Hudson's  Bay,  and  the 
south  magnetic  pole  is  in  a  corresponding  position  south 
of  Australia. 

427.  The  nature  of  the  influence  which  magnets  exert  over  bars 
of  iron  and  steel  to  polarize  their  particles  and  make  magnets  of  them, 
as  explained  in  Art.  416,  is  little  understood.  We  shall  find  in  a  suc- 
ceeding chapter,  however,  that  there  is  a  close  connection  between 
magnetic  phenomena  and  the  existence  of  electric  currents.  A  sub- 
ject of  much  interest  awaits  us. 


1  Alexander  von  Humboldt,  German,  1769-1859.  An  illustrious 
traveller,  and  an  eminent  scholar  in  many  branches  of  learning.  An 
authority  on  most  scientific  subjects. 


ELECTRICITY.  255 


CHAPTEE  IX. 

ELECTRICITY. 
I,— FRICTIONAL   ELECTRICITY. 

428.  Electrical  Phenomena. — It  was  known  to  the  an- 
cients that  amber  rubbed  with   some  soft  material  pos- 
sessed the  power  of  attracting  light  bodies.     It  has  since 
been  discovered  that  many  other  substances  exhibit  the 
same  property.      The  Greek  name  of  amber  is  elektron; 
hence  the  name  electricity  came  to  be  applied  to  the  force 
thus  developed,  whether  in  amber  or  in  any  other  sub- 
stance.    A  gutta-percha  comb,  after  being  drawn  through 
dry  hair,  in  cool,  dry  weather,  will  pick  up  small  tufts  of 
cotton,  pieces  of  paper,  scraps  of  corn-stalk-pith,  or  any 
similar  light  substance.     A  sheet  of  thin  paper  rubbed  with 
an  eraser  adheres  tightly  to  the  sheet  under  it,  or  to  a  wall. 
The  force  which  holds  these  bodies  together  is  electricity. 

429.  Note. — Apparatus  Needed. — The  following  small  articles 
will  be  needed  frequently  in  trying  electrical  experiments,  and  should 
be  kept  on  hand.     Two  glass  rods,  or  heavy  tubes,  about  15  inches 
long,  and  at  least  f  of  an  inch  in   diameter  ;   two  smaller  rods  of 
shellac  (sealing-wax  or  gutta-percha  may  be  substituted  for  shellac)  ; 
a  silk  pad,  made  by  quilting  together  from  three  to  six  pieces  of  silk, 
about  8  inches  square  ;  a  similar  pad  of  flannel,  or  a  cat's  skin  tanned 
with  the  fur  on  (a  silk  handkerchief  and  a  flannel  cloth  will  do) ;  a 
lot  of  pith-balls  from  }  to  £  inch  in   diameter,  made  by  cutting  the 
dried  pith  of  corn-stalks  into  shape  with  a  sharp  knife ;  a  spool  of 
sewing-silk  ;  a  spool  of  thread  ;  a  few  bottles  and  other  glass  vessels  ; 
a  supply  of  corks,  pins,  needles,  wax. 

In  addition  to  these,  a  class  should  have  a  proof-plane  and  an  electro- 
scope. They  are  easily  made.  The  proof-plane  is  a  circular  piece  of 
tin  about  two  inches  in  diameter,  with  a  piece  of  glass  tube  or  a  gutta- 
percha  pen-holder  stuck  to  it  with  sealing-wax,  for  a  handle.  A  very 
good  electroscope  may  be  made  as  follows  (see  Fig.  257).  Procure  a 
wide-mouthed  jar  of  about  a  quart  capacity ;  paste  on  the  inside,  on 


256  NATURAL  PHILOSOPHY. 


opposite  sides  of  the  jar,  two  strips  of  tin-foil  3  inches  long  and  1  inch 
wide.  These  should  extend  upward  from  the  bottom  of  the  jar. 
Have  a  cork  to  fit  the  jar,  and  pass  through  it  a  stout  wire.  Make  a 
stirrup  on  the  lower  end  of  the  wire,  say  two  inches  from  the  cork. 
If  convenient,  solder  to  the  upper  end  of  the  wire  a  circular  tin 
plate  of  the  same  size  as  the  proof-plane.  Hang  in  the  stirrup  by 
the  middle  a  piece  of  thin  gold-leaf  4  or  5  inches  long  and  J  inch 
wide.  It  may  be  bought  of  a  dealer  in  chemicals,  or  of  a  dentist,  for 
a  few  cents,  but,  if  it  is  not  at  hand,  take  silver-leaf,  gilt  paper,  or 
very  thin  tin-foil  instead.  Be  sure  that  the  bottle  is  dry.  Insert  the 
cork,  and  run  melted  wax  over  it.  The  gold-leaves  should  open 
towards  the  strips  of  tin-foil. 

In  trying  experiments  in  electricity  all  apparatus  must  be  dry,  and 
it  should  be  warmed  by  the  stove  frequently  while  being  used.  Much 
of  the  glass  of  commerce  contains  metallic  impurities,  which  render 
it  unfit  for  electrical  experiments.  If  failures  occur,  when  every- 
thing seems  right,  try  new  glass.  "  Bohemian"  glass  has  given  the 
writer  the  most  satisfaction. 

Experiments  in  frictional  electricity  succeed  best  in  crisp  winter 
weather,  when  the  atmosphere  contains  but  little  moisture.  In  sum- 
mer weather  it  is  sometimes  difficult  or  impossible  to  produce  electrical 
excitement. 

430.  Electrical  Attraction,— Experiment  157.— Grasp  a  glass 
rod  near  one  end  and  rub  it  briskly  with  the  silk  pad.     A  crackling 
noise  and  a  sensation  as  of  cobwebs  on  holding  the  rod  near  the  face 
indicate  that  it  is  electrified.    Hold  it  near  a  light  rubber  ball  placed 
on  a  smooth  table.  The  ball  will  be  attracted,  and  will  follow  the  rod 
around  the  table  several  times.    A  round  collar-box  or  a  hoop  of  any 
light  material  will  answer  equally  well.     Rub  a  rod  of  shellac  with 
the  flannel  and  present  it  to  the  ball  or  the  hoop.     The  same  result 
will  follow. 

431.  Attraction  and  Repulsion. — Experiment   158.— Make  a 

"wire  loop"  (such  as  is  shown  in  Fig. 
255)  of  sufficient  size  to  hold  the  glass 
and  shellac  rods.  Suspend  it  by  a  silk 
thread  or  narrow  ribbon  to  a  convenient 
support.  Rest  in  it  one  of  the  glass 
rods.  Rub  the  other  rod  with  the  silk, 
and  bring  it  near  the  suspended  rod. 
There  will  be  an  attraction.  Repeat 
the  experiment,  but  this  time  rub  the 
first  rod  before  placing  it  in  the  loop. 
On  presenting  the  other  glass  rod, 
freshly  rubbed,  there  will  be  a  re- 
pulsion. 

Follow  the  same  course  with  the  rods 
Fia.  255.— WIRE  LOOP.          of  shellac  rubbed  with  flannel.     They 
will  act  in  the  same  way.     Remove  the 

electrical  excitement  from  the  surface  of  one  of  the  shellac  rods  by 
drawing  it  through  the  hand.  Place  it  in  the  loop  and  present  a 
freshly-rubbed  glass  rod.  There  will  be  attraction.  Rub  the  shellac 
rod  and  again  present  the  rubbed  glass.  There  will  still  be  attraction. 


ELECTRICITY.  257 


432.  Two  Kinds  of  Electricity.  —  The  last   experiment 
shows  that  the  two  electrified    bodies,  though   behaving 
similarly  towards  the  unelectrified  indicator,  are  different 
manifestations  of  the  same  force.   It  recalls  the  experiment 
which  proved  the  difference  between  the  two  poles  of  a 
magnet.     Here,  however,  both  ends  of  the  electrified  body 
are  similar.     It  is  the  electric  states  of  the  two  bodies,  the 
glass  and  the  shellac,  which  are  dissimilar.   For  distinction, 
the  electric  force  developed  on  smooth  glass  by  rubbing  it 
with  silk  is  called  positive  electricity,  and  that  developed  on 
shellac  by  rubbing  it  with  flannel  is  called  negative  electricity. 
These  are  old  names,  and  the  theory  which  gave  rise  to 
them  has  been  abandoned,  but,  as  they  have  very  distinct 
applications  and  are  frequently  used,  they  must  be  remem- 
bered and  distinguished.     The  friction  of  many  other  sub- 
stances produces  electricity,  but  it  all  proves  itself  to  belong 
to  one  or  the  other  of  the  above  classes. 

The  sign  -f  is  used  in  many  of  the  figures  which  occur  in  this 
chapter  to  denote  positive  electricity,  and  the  sign  —  to  denote  nega- 
tive electricity.  These  are  not  to  be  read  plus  and  minus,  but  positive 
and  negative. 

433.  Law  of  Attraction  and  Repulsion.— Experiment  158 
will  have  suggested  the  following  law :    The  two  kinds  of 
electricity  attract  each  other,  but  each  is  self-repellent. 

434.  No  reason  has  been  discovered  why  one  body  should 
exhibit  positive  electricity  and  another  negative.     When  a 
substance  whose  nature  is  unknown  is  electrified,  it  must 
be  tested  by  one  whose  electricity  is  known.     To  test  a 
body,  ascertain  whether  excited  glass  or  excited   shellac 
repels  it. 

435.  What  is  Electricity  ?— We  might   further  say   that  no 
reason  has  been  discovered  why  a  body  should  be  electrified  at  all. 
Electricity  is  a  state  of  strain  which  a  body  exhibits  as  an  equivalent 
of  the  energy  applied  to  produce  it      It  is  a  complete  example  of  the 
conservation  of  energy.     In  the  experiments  which  we  have  thus  far 
tried,  the  energy  applied  in  the  rubbing  of  the  rod  appears  as  a  force 
in  the  rubbed  rod  capable  of  moving  light  bodies.     We  shall  see, 

r  22* 


258  NATURAL   PHILOSOPHY. 

as  we  proceed,  that  it  is  capable  of  reappearing  as  energy  of  other 
kinds. 

436.  To  Charge  a  Body.— Experiment  159.— To  each  end  of  a 

silk  thread  two  feet  long  attach  a  pith  ball, 
and  suspend  the  silk  by  the  middle.  Hub  a 
glass  rod  with  silk  and  touch  it  to  the  balls 
as  they  hang  together.  They  will  now  repel 
each  other  and  stand  apart  for  a  considerable 
time. 

This  experiment  shows  that  elec- 
tricity passes  from  one  body  to  an- 
other. Each  ball  has  taken  some 
of  the  positive  electricity  from  the 
glass,  and  the  two,  being  similarly 
electrified,  repel  each  other.  A  body 
FIG.  256,-ELECTRicAL  RE-  which  has  taken  some  electrical  force 
from  another  is  said  to  be  charged; 

a  body  which  has  been  electrified  by  friction  is  said  to  be 

excited. 

437.  Neutral  and  Excited  Bodies.— If  the  excited  glass 
and  the  excited  shellac  be  rubbed  or  rolled  thoroughly  over 
each  other,  each  will  lose  the  principal  part  of  its  charge, 
This  leads  us  to  conclude  that  each  is  capable  of  undoing 
or  neutralizing  the  electric  state  of  the  other.     This  is  ex- 
pressed by  saying  that  the  two  electricities  will  unite  with 
each  other.     If  the  positive  charge  of  one  body  and  a  cor- 
respondingly heavy  negative  charge  of  another  body  unite, 
neither  body  manifests  electrical  excitement  after  the  union. 
The  bodies  may  then  be  said  to  be  neutral.     Nearly  all 
bodies  capable  of  electrical  excitement  are  usually  in  a 
non-excited  state.     We  may  express  this  by  saying  that 
the  two  electricities  neutralize  each  other  in  such  bodies. 
When  they  are  excited  by  rubbing,  the  rubbed  body  exhibits 
one  kind  of  electricity  and  the  rubber  the  other  kind.     Try 
the  following : 

Experiment  160. — Rub  a  glass  rod  with  the  silk  pad  (holding  the 
pad  in  a  piece  of  sheet-rubber,  e.g.,  the  top  of  an  old  overshoe),  and 
present  the  pad  to  some  light  pieces  of  feather  or  something  of  the 


ELECTRICITY.  259 


kind.  There  will  be  an  attraction,  showing  that  the  pad  is  electrified. 
Kub  the  rod  again,  and  suspend  it  as  in  Experiment  158.  The  pad 
and  the  rod  will  attract  each  other,  showing  that  they  are  differently 
electrified.  The  neutral,  inactive  electricities  of  the  two  bodies  were 
roused  up  in  some  manner  by  the  rubbing,  and  arrayed  themselves 
against  each  other,  part  of  the  negative  of  the  glass  going  to  the  pad, 
and  part  of  the  positive  of  the  pad  going  to  the  glass. 

Experiment  161. — To  show  that  the  two  electricities  do  exist  in  the 
glass  before  excitement,  rub  a  glass  rod  with  flannel,  or,  better,  on  a 
cat's  skin.  It  will  repel  excited  shellac,  indicating  that  it  is  negatively 
electrified.  To  procure  positive  electricity  on  glass,  be  sure  to  rub  it 
with  silk.1 

438.  Conductors  and  Insulators.— If  an  excited  rod  be 
touched  to  one  end  of  a  metal  bar,  an  indicator  at  the 
other  end  shows  that  the  electric  force  is  immediately  felt 
there.  If  the  same  experiment  be  tried  with  a  glass  bar, 
the  electricity  does  not  manifest  itself  to  any  appreciable 
extent  at  the  farther  end.  Substances  which  readily  trans- 
mit electricity  are  called  conductors.  The  metals,  charcoal, 
wood,  water,  hemp,  and  animal  bodies  are  conductors. 
Two  or  more  bodies  connected  by  conductors  are  said  to 
be  in  electrical  connection. 

Substances  which  transmit  electricity  feebly,  or  not  at 
all,  are  called  insulators,  and  a  body  in  contact  with  nothing 
but  insulators  is  said  to  be  insulated.  Dry  air,  shellac,  rosin, 
beeswax,  glass,  india-rubber,  and  silk  are  among  the  most 
common  insulators.  As  the  human  body  is  a  conductor,  it 
is  evident  that  we  should  handle  all  electrified  bodies  by 
means  of  insulating  handles  if  we  would  have  them  retain 
their  electrical  condition.  Particles  of  dust  and  moisture 
which  may  collect  on  insulators  have  some  power  of  con- 

1  When  we  speak  of  "  two  electricities  existing  in"  a  body,  we  are 
using  language  rather  loosely,  as  electricity  is  not  a  substance,  but  a 
force.  It  would  be  more  accurate  to  say  that  a  body  is  capable  of 
exhibiting  either  phase  of  the  electric  force ;  but  we  could  not  de- 
scribe the  experiments  in  the  more  strict  language  without  making 
very  tiresome  sentences,  so  philosophers  agree  to  use  the  simpler 
expressions  for  convenience,  and  ask  their  students  not  to  picture  to 
themselves  electricity  as  a  material. 


260  NATURAL   PHILOSOPHY. 

duction :  hence  the  caution  to  keep  all  electrical  apparatus 
while  in  use  clean  and  warm. 

439.  Electrical  Induction. — As  a  magnet  may  communi- 
cate its  power  of  attraction  to  a  piece  of  iron  at  a  short 
distance  from  it,  so  an  electrified  body  may  induce  electrical 
excitement  in  another  body  without  touching  it. 

Experiment  162. — Bring  the  excited  glass  or  shellac  rod  near  the 
knob  or  plate  of  the  gold-leaf  electro- 
scope (Art.  429).  As  it  approaches  the 
leaves  will  diverge,  and  as  it  recedes  the 
leaves  will  come  together.  Kepeat  sev- 
eral times  in  succession. 


The  gold-leaves  in  this  experi- 
ment were  similarly  electrified  by 
induction,  hence  they  repelled  each 
other.  For  a  full  understanding 
of  many  of  the  phenomena  which 
FIG.  257,-GoLD-LEAF  ELEC-  we  are  aDOut  to  study,  it  is  neces- 
sary  for  us  to  bear  constantly  in 

mind  that  any  excited  body  tends  to  excite  by  induction  insulated 
bodies  near  it.  It  is  also  essential  that  we  should  be  able  to 
tell,  in  any  case,  what  kind  of  electricity  one  body  induces  in 
another,  or  in  different  parts  of  it. 

Experiment  163. — Touch  the  proof-plane  (Art.  429)  to  an  excited 
glass  rod,  and  then  to  the  top  of  the  gold-leaf  electroscope.  The 
leaves  become  charged,  and  remain  diverging  after  the  proof-plane  is 
withdrawn.  Carry  a  second  charge  from  the  glass  to  the  gold-leaves. 
They  diverge  more  widely.  While  they  are  still  divergent,  carry  to 
them  with  the  proof-plane  a  charge  from  excited  shellac.  The  nega- 
tive electricity  neutralizes  some  or  all  of  the  positive  in  the  leaves, 
and  they  fall  towards  each  other. 

440.  To  Test  the  Kind  of  Electricity. — This  experiment 
indicates  how  we  are  to  test  the  kind  of  electricity  on  any 
excited  surface.  Diverge  the  gold-leaves  with  a  known 
kind.  While  they  are  still  divergent,  the  contact  of  a  body 
similarly  electrified  produces  more  divergence,  and  the  con- 
tact of  a  body  oppositely  electrified  produces  less  divergence. 


ELECTRICITY.  261 


441.  Body  electrified  by  Induction.— Experiment  164.— Pro- 
cure or  make  a  cylinder  whose  length  is  about  four  times  its  diame- 
ter. Eight  and  two  inches 
are  very  convenient  di- 
mensions for  these  experi- 
ments, though  very  much 
smaller  will  do,  and  very 
much  larger  are  better 
when  we  have  much  elec- 
tricity. The  ends  must 
be  convex,  as  shown  in 
Fig.  258.  The  outside  of 
the  cylinder,  ends  and  all, 
must  be  of  some  conduct- 
ing material.  Turned 
wood  covered  with  tin-foil  Fl<*.  258.— INDUCTION  CYLINDER. 

answers    admirably.      A 

hollow  tin  can  with  round  ends  would  be  good.  An  egg,  an  apple, 
a  croquet-ball,  would  do.  This  is  an  induction  cylinder.  Support  it 
on  glass  or  wax,  or  hang  it  by  silk.  Hold  an  excited  rod  near  one 
end.  While  it  is  held  there,  touch  first  one  end  and  then  the  other  of 
the  induction  cylinder  with  the  proof-plane,  and  test  each  with  the 
gold-leaves.  The  end  next  to  the  excited  rod  will  be  found  in  the 
electrical  state  opposite  to  that  of  the  rod,  and  the  farther  end  will  be 
found  similar  to  the  rod.  Try  the  middle  of  the  cylinder.  It  will 
be  found  neutral. 


442.  Cause  of  Attraction  by  an  Electrified  Body.— All 

bodies  electrified  by  induction  show  the  above  result.  The 
electrifying  body  attracts  the  opposite  and  repels  the  simi- 
lar electricity,  in  accordance  with  Art.  433.  This  brings 
us  to  an  important  principle  of  electrical  attraction, — viz., 
a  body  attracted  by  an  electrified  surface  is  first  electrified  by 
induction,  and  the  apparent  attraction  of  the  bodies  is  really 
the  attraction  of  the  opposite  hinds  of  electricity. 

443.  Why  a  Body  is  charged. — The  body  which  electri- 
fies another  by  induction  does  not  thereby  lose  any  of  its 
charge ;  but  if  a  body  which  is  electrified  be  brought  into 
contact  with  one  which  is  not,  the  electrified  body  does  lose 
some  of  its  electricity.     Suppose  the  first  body  to  be  posi- 
tively electrified.     Part   of  the   positive   electricity  com- 
bines with  the  negative  which  has  accumulated  on   the 
nearest  part  of  the  other  body.      The  farther  extremity 
of  the  second  body  remains  positively  electrified  by  repul- 


262  NATURAL  PHILOSOPHY. 

sion.  When  the  electrifying  body  is  withdrawn,  this  posi- 
tive electricity  disposes  itself  symmetrically  over  the 
surface  of  the  body,  and  the  body  is  charged. 

444.  Insulators   easily  charged. — It  will  have  been  no- 
ticed by  the  pupil,  before  reaching  this  point,  that  the  sub- 
stances upon  which  we  develop  electricity  are  insulators. 
This  is  largely  because  glass,  shellac,  etc.,  are  easily  ex- 
cited, but  partly  because  the  very  fact  of  their  being  insu- 
lators enables  them  to  retain  the  charge  which  is  developed 
on  their  surface.     When  any  point  of  a  charged  conductor 
is  placed  in  electrical  connection  with  another  conductor 
of  very  large  size  (the  earth,  for  example),  the  whole  charge 
passes  off,  and  the  body  is  said  to  be  discharged.     In  order 
to  discharge  a  charged  insulator,  all  parts  of  its  surface  must 
be  placed  in  electrical  connection  with  a  large  conductor. 

445.  Action  of  Points. — Before  going  into  the  study  of 
electrical  machines  it  will  be  necessary  to  observe  and  re- 
member the  effect  of  pointed  conductors  on  a  charge  of 
electricity. 

Experiment  165. — Touch  an  insulated  cylinder  (see  Fig.  258)  with 
an  electrified  body.  While  the  balls  are  divergent,  point  a  needle 
or  an  open  penknife  towards  it.  The  balls  will  fall  together,  and  re- 
main so  after  the  point  is  withdrawn. 

446.  The  Earth  is  the  Great  Reservoir  of  electricity,  both 
positive  and  negative.     A  person  standing  on  an  ordinary 
floor  is  in  electrical   connection  with  the  earth.     An  elec- 
trified body  tends  to  draw  towards  it  the  opposite  elec- 
tricity of  any  object  sufficiently  near.     (Art.  441.)     When 
the  surfaces  are  curved,  as  in  the  induction-cylinder,  the 
electricity,  though  attracted  by  the  inducing  body,  is  kept 
back  by  the  insulating  air,  a  large  surface  of  which  is  op- 
posed to  the  electricity,   and  thus  prevents   its  passage. 
When  the  surface  at  the  place  to  which  the  electricity  is 
drawn  by  induction  is  very  small,  as  the  needle-point,  the 
air  can  oppose  but  little  resisting  surface,  and  the  elec- 
tricity flies  across  the   insulating  space  to  the  inducing 


ELECTRICITY. 


263 


body.  If  the  point  be  attached  to  an  insulated  conductor, 
instead  of  being  held  in  the  hand  of  a  person  standing  on 
the  floor,  the  conductor  will  be  found  charged  with  one 
kind  of  electricity  by  the  escape  of  the  opposite  kind  from 
the  point. 

447.  The  Electric  Spark. — When  a  charge  of  electricity 
is  sufficiently  intense,  it  will  pass  through  an  insulator  from 
one  conductor  to  another  though  the  surfaces  be  round  and 
smooth.     Such  a  charge,  in  passing  through  the  insulating 
medium  (mostly  air),  produces  the  electric  spark. 

448.  Electrical  Machines.— We  have  now  learned  all  the  prin- 
ciples involved  in  the  construction  of  electrical  machines,  and,  as 
many  experiments  succeed  best  when  an  electrical  machine  is  used, 
we  shall  describe  a  few  common  forms. 

449.  The  Plate  Electrical  Machine.— The  circular  glass  plate 

G  (Fig.  259)  is  clamped  to  the  axle  and  turned  by  the  handle.     The 


Fia.  259. — PLATE  ELECTRICAL  MACHINE. 


arrow  shows  the  direction  of  rotation.  Two  rubbers  at  K  are  pressed 
by  springs  agairst  opposite  sides  of  the  plate.  These  springs  are  con- 
nected with  the  ball  N,  which  is  insulated  on  glass  and  forms  the 


264  NATURAL  PHILOSOPHY. 


negative  conductor.  On  the  opposite  side  of  the  plate  is  the  positive 
or  prime  conductor  P,  also  on  an  insulating  support.  The  combs  C 
are  the  points  over  which  the  negative  electricity  is  to  flow  to  the 
glass  plate.  They  are  of  brass.  The  rubbers  may  be  chamois-skin 
coated  with  "  electrical  amalgam."  (This  is  a  compound  similar  to 
the  coating  on  a  looking-glass.  The  rubbers  have  tallow  spread  over 
the  face,  and  the  amalgam  is  spread  evenly  over  this.) 

When  the  handle  is  turned,  the  friction  of  the  rubbers  develops 
positive  electricity  on  the  surface  of  the  glass  and  negative  on  the 
rubbers.  The  negative  conductor  thus  becomes  charged.  As  the 
rubbers  are  expected  to  take  an  unlimited  quantity  of  negative  elec- 
tricity, it  must  be  constantly  carried  away  to  the  earth,  or  neutralized 
by  positive  from  the  earth,  or  from  the  prime  conductor.  As  we 
generally  wish  to  use  the  positive  electricity,  we  connect  the  negative 
conductor  with  the  ground  by  a  chain  dropped  on  the  floor,  or,  better, 
attached  to  a  stove- foot  or  a  gas-  or  water-pipe. 

When  the  plate  with  its  positive  electricity  has  turned  half-way 
round,  it  acts  by  induction  on  the  prime  conductor,  drawing  the  nega- 
tive towards  it  and  repelling  the  positive  to  the  other  extremity.  At 
C  the  negative  electricity  finds  the  points  of  the  "  comb"  and  rapidly 
escapes  to  the  glass,  neutralizing  the  positive  on  its  surface.  The 
positive  electricity  on  the  prime  conductor  finds  rounded  surfaces,  and 
remains  till  it  becomes  of  considerable  intensity.  This  action  is  con- 
tinuous as  long  as  the  handle  is  turned.  The  lower  half  of  the  plate 
is  always  positively  electrified.  The  upper  half  is  neutral.  Positive 
electricity  may  be  drawn  from  any  part  of  the  prime  conductor  while 
the  machine  is  worked,  but  it  is  more  intense  towards  the  outer  end 
(the  small  ball  in  the  machine  here  shown).  The  excellence  of  a 
machine,  or  of  atmospheric  conditions,  is  determined  by  the  distance 
the  charge  will  pass  through  the  air,  as  a  spark,  from  the  end  of  the 
prime  conductor  to  the  knuckle  of  the  operator  or  some  other  convex 
conductor.  This  distance  is  called  the  length  of  the  electric  spark. 

If  we  wish  to  use  the  negative  electricity  from  the  machine,  the 
ground-connection  is  made  with  the  prime  conductor.  The  negative 
spark  is  much  shorter  and  less  intense  than  the  positive.  Connection 
may  be  made  between  the  two  conductors.  In  this  case  the  two 
kinds  of  electricity  will  neutralize  each  other,  and  the  earth-supply 
will  not  be  needed. 

450.  The  Cylinder  Machine. — Fig.  260  represents  a  cylinder 
machine,  which  is  much  less  expensive  than  a  plate  machine.  Any 
school-boy  may  make  one.  A  large  bottle  (one  that  would  hold  from 


ELECTRICITY. 


265 


one  to  four  quarts)  will  answer  for  the  cylinder.  A  glass  rod,  G, 
supports  the  prime  conductor,  C.  This  may  be  of  wood,  covered 
with  tin-foil.  Let  the  tin-foil  extend  so  far  as  to  the  pin-points,  P. 


FIG.  260. — CYLINDER  ELECTRICAL  MACHINE. 

R  is  the  rubber,  made  of  leather,  or  chamois,  or  silk,  stuffed  with 
wool.  A  silk  apron,  S,  attached  to  the  rubber  and  extending  over 
the  cylinder,  adds  to  the  certainty  of  its  working.  The  rest  of  the 
machine  is  of  dry  wood. 

451.  Other  Electrical  Machines. — For  explanations  of  many 
other  interesting  forms  of  electrical  machines  the  reader  is  referred 
to  more  extended  works  on  Natural  Philosophy.     The  Holtz  induc- 
tion machine,  and  the  Armstrong  hydro-electric  or  steam  electrical 
machine,  are  both  capable  of  developing  electricity  in  prodigious 
quantities. 

Note. — "With  either  of  the  devices  explained  above,  most  of  the  fol- 
lowing experiments  may  be  made  to  succeed  in  good  weather.  If  the 
machine  is  home-made,  be  sure  there  are  no  sharp  corners  or  loose 
edges  of  tin-foil  where  they  would  allow  the  charge  to  escape.  Grind 
off  edges  of  thick  metal,  and  carefully  press  down  with  the  finger-nail 
all  edges  of  tin-foil.  A  coat  of  varnish  helps  insulators  to  keep  dry. 

452.  Experiments  in  Attraction  and  Repulsion.— Experi- 
ment 166. — To  the  top  of  a  stem  of  wood  hinge  a  slender  wooden 
toothpick,  so  that  it  will  move  in  an  arc  of  90°.    Stick  the  free  end  of 
the  toothpick  into  a  pith  ball.     A  paper  scale  may  be  attached,  as 
shown  in  Fig.  261.     This  is  a  quadrant  electrometer.     Stand  it  up  in 
a  gimlet-hoie  carefully  bored  in  the  top  of  the  prime  conductor.     It 

M  23 


266 


NATURAL   PHILOSOPHY. 


indicates,  by  the  rising  of  the  pith  ball,  the  presence  of  electricity  in 
the  conductor. 

Experiment  167.— Hang  from  the  end  of  the  prime  conductor  a 
round  metal  plate  by  the  centre.  Hold  under  it  a  similar  plate  on 
which  are  placed  a  few  paper  or  pith  images.  When  the  machine  is 
operated,  the  images  will  dance  vigorously  between  the  plates.  Vary 
this  experiment  by  supporting  the  lower  plate  on  glass.  Explain 
both  phenomena. 


FIG.  261.— QUADRANT  ELECTROMETER. 


FIG.  262.— ELECTRICAL  CHIMB. 


Experiment  168. — Suspend  three  bells,  as  shown  in  Fig.  262.  Any 
bells  will  do.  Suspend  those  at  the  end  by  conductors,  and  the  middle 
one  by  silk.  Suspend  two  little  metal  clappers  by  silk.  Let  a  chain 
or  wire  drop  from  the  middle  bell  to  the  floor.  Operate  the  machine 
and  hear  the  result. 

Experiment  169. — Suspend  a  light  figure  of  a  boy  in  a  silk  swing 
a  foot  long.  Arrange  the  swing  so  that  the  figure  will  hang  midway 
between  the  prime  conductor  and  a  metal  knob,  or  a  knuckle  held  a 
few  inches  distant.  Let  the  machine  be  turned.  Devise  a  see-saw,  a 
pump-handle,  or  a  man  sawing  wood  to  be  operated  by  electricity. 

Experiment  170. — Grind  to  a  point  a  stout  wire  six  inches  long. 
Bend  the  wire  at  right  angles  near  the  point.  Insert  the  other  end 
into  the  hole  in  the  prime  conductor.  When  the  machine  is  worked, 
hold  a  lighted  candle  at  the  point  of  the  wire.  The  flame  is  blown 
from  the  point.  This  is  because  the  molecules  of  the  air  are  succes- 
sively charged  by  the  electricity  of  the  point,  and  are  repelled  from  it. 

Experiment  171. — Stick  four  or  six  of  these  sharpened  and  bent 
wires  into  a  cork,  so  that  they  will  all  be  in  the  same  plane  and  bal- 
ance horizontally.  Insert  a  thimble  or  a  lamp-extinguisher  in  the 
cork,  and  push  the  wires  in  against  it.  Balance  on  a  straight  sharp 
wire  which  stands  in  the  hole  in  the  prime  conductor.  The  points 
and  the  molecules  of  air  repel  each  other,  causing  the  "  flyer"  to  re- 
volve (Fig.  263). 

Experiment  172. — -Cut  a  large  number  of  very  narrow  strips  of 
thin  paper.  Bind  them  together  at  one  end  by  a  wire,  and  hang  on 
the  prime  conductor.  Turn  the  machine. 


ELECTRICITY. 


267 


Experiment  173. — Make  a  very  small  hole  in  the  bottom  of  a 
tomato-can.  Partly  fill  the  can  with  water,  and  hang  on  the  prime 
conductor  by  a  wire.  If  the  water  drops 
slowly  from  the  hole  before  the  machine  is 
operated,  it  will  be  forced  out  in  a  diverg- 
ing spray  on  the  turning  of  the  handle. 


453.  The  Electrophorus,  Fig.  264,  is 

a  very  simple  and  at  the  same  time  a  very 
instructive  instrument  sometimes  used  for 
the  development  of  electricity.  Any  boy 
or  girl  may  make  one.  The  lower  disk, 
OT  plate,  is  of  resin,  which  has  been  melted 
and  poured  into  a  tin  vessel  a  half-inch 
deep,  and  a  foot,  more  or  less,  in  diameter. 
A  tinsmith  will  furnish  both  the  vessel  and 
the  resin  (rosin).  The  lid  is  of  metal,  or 
of  wood  covered  with  tin-foil.  It  must  be 
rather  smaller  than  the  plate.  The  handle  is  of  glass  or  sealing-wax. 


FIG.  263.— ELECTRICAL  FLYER. 


Experiment  174.  —  Stroke  the  plate  of  the  electrophorus  with  a  cat's 
skin  or  a  piece  of  flannel.  It  will  be  negatively  electrified.  Holding 
the  lid  by  the  insulating  han- 
dle, place  it  flat  on  the  plate. 
After  a  moment's  contact,  re- 
move it,  and  test  with  the  elec- 
troscope. It  is  not  appreciably 
electrified.  Place  the  lid  on 
the  plate  again,  and  touch  it 
with  the  finger  before  remov- 
ing it  by  the  insulating  han- 
dle. After  it  is  lifted  from 
the  plate,  touch  it  with  a 
knuckle  of  the  other  hand. 
A  spark  will  pass,  showing 
that  it  is  charged.  Charge 
the  lid  again,  and  try  it  with 
the  proof-plane  and  electro- 
scope. Its  electricity  is  posi- 
tive. 


FIG.  264.— THE  ELECTROPHORUS. 


Be  sure  to  understand 
the  action  of  the  electro- 
phorus before  going  further.  It  opens  the  way  for  easily 
understanding  the  Leyden  (ll'den)  jar  and  other  condensers 
of  electricity.  When  the  lid  was  placed  on  the  excited  plate 
by  the  insulating  handle,  the  neutral  condition  of  the  lid 


268  NATURAL   PHILOSOPHY. 

was  undone  by  the  inductive  action  of  the  plate.  Its  posi- 
tive was  drawn  to  the  surface  next  to  the  plate,  and  its 
negative  repelled  to  the  upper  surface.  When  the  lid  was 
lifted  by  the  insulating  handle  without  having  been  touched 
by  the  finger,  the  two  kinds  of  electricity  reunited  and 
neutralized  each  other  as  soon  as  the  lid  was  out  of  reach 
of  the  inductive  influence  of  the  plate.  In  the  other  case, 
when  the  lid  was  touched  by  the  finger,  the  repelled  nega- 
tive electricity  found  a  way  to  the  earth  and  escaped. 
Then,  when  the  lid  was  lifted  by  the  handle,  the  positive, 
having  no  negative  to  unite  with,  diffused  itself  over  the 
surface  as  a  charge.  The  important  principle  which  the 
electrophorus  illustrates  is  that  when  a  body  is  electrified 
by  induction,  the  attracted  electricity  is  bound,  and  the  re- 
pelled electricity  is  free.  To  render  this  more  apparent, 
touch  the  proof-plane  to  the  lid  as  it  lies  on  the  plate,  both 
before  and  after  it  has  been  touched  by  the  finger.  The 
electroscope  detects  negative  electricity  in  the  first  case, 
and  no  charge  in  the  second  case. 

In  the  electrophorus  we  are  to  consider  a  thin  layer 
of  air  between  the  lid  and  the  plate,  except  at  the  com- 
paratively few  points  of  contact.  The  resin  being  a  non- 
conductor, the  positive  electricity  of  the  lid  cannot  pass 
to  the  surface  of  the  plate  by  way  of  these  points,  so 
it  is  simply  held  as  near  the  plate  as  possible.  The  lid 
may  be  repeatedly  charged  from  the  plate  after  it  has 
been  once  excited,  which  would  be  impossible  if  the  lid, 
touched  by  the  finger,  came  in  contact  with  the  whole 
plate.  Although  air  is  an  insulator,  a  very  thin  layer 
of  it  offers  but  feeble  resistance,  so  that  no  considerable 
charge  can  thus  be  obtained.  A  thin  layer  of  glass  offers 
much  more  resistance  to  the  passage  of  electricity  than 
the  same  amount  of  air  does,  but  it  does  not  interfere  with 
induction.  Two  conductors  separated  by  glass,  may  there- 
fore be  heavily  charged  with  the  two  kinds  of  electricity, 
each  holding  the  other  bound,  and  neither  showing  its 


ELECTRICITY. 


269 


presence  when  tested  by  a  neutral  body.   Such  an  arrange- 
ment is  called  a  condenser. 

454.  The  Leyden  Jar. — The  most  common  form  of  condenser  is 
the  Leyden  jar,  so  called  because  the  discovery  which  led  to  its  con- 
struction was  made  at  Leyden  about  the  middle  of  last  century.  As 
bought  of  an  instrument-maker,  it  consists  of  a  glass  jar  (see  Fig. 
265)  with  coatings  of  tin-foil  inside  and  out,  covering  the  bottom,  and 


FIG.  265. — DISCHARGING  LEYDEN  JAR. 

the  sides  about  two-thirds  of  the  way  to  the  top.  A  rod,  piercing  the 
cork,  ends  above  in  a  ball  or  ring,  and  below  in  a  chain  or  wire 
reaching  to  the  bottom  of  the  jar.  To  charge  the  jar,  take  it  in  one 
hand  by  the  outside  coating.  Present  the  knob  to  the  prime  con- 
ductor. Sparks  of  positive  electricity  pass  from  the  conductor  to 
the  ball,  and  so  to  the  inside  coating.  Each  spark  of  positive  thus 
conveyed  to  the  inside  surface  of  the  jar  holds  bound  against  the  out- 
side surface  a  corresponding  amount  of  negative,  and  repels  its  own 
amount  of  positive  through  the  arm  and  body  of  the  operator.  A 
large  number  of  sparks  may  thus  be  passed  into  the  jar,  each  one 
increasing  the  amount  of  positive  on  the  inside  and  the  amount  of 
negative  on  the  outside,  till  the  tension  approaches  its  limit,  when 

23* 


270  NATURAL  PHILOSOPHY. 


the  sparks  become  noticeably  less  vigorous.  The  jar  is  now  charged, 
and  if  a  conductor  is  made  to  reach  from  any  point  of  the  outside 
coating  to  the  knob,  the  two  kinds  of  electricity  unite  with  great 
energy.  This  is  discharging  the  jar.  An  experimenter  uses  for  this 
purpose  a  bent  or  jointed  rod  with  an  insulating  handle.  Fig.  265 
shows  an  ordinary  Leyden  jar  and  a  jointed  discharger.  A  heavy 
bent  wire,  with  rings  formed  on  the  ends,  will  do.  The  discharge  in 
this  way  is  instantaneous.  If  a  body  capable  of  taking  a  small 
charge  of  electricity  is  suspended  by  a  silk  thread  between  two  con- 
ductors which  are  in  electrical  connection  with  the  two  coats  of  the 
jar,  it  will  carry  successive  charges  of  positive  to  the  outside  coat, 
and  of  negative  to  the  inside  coat,  until  the  two  are  neutralized  in 
both.  The  little  clapper  shown  in  Fig.  266  will  swing  between  the 
bells  and  keep  up  a  chime  for  an  hour,. under  favorable  conditions. 


FIG.  266. — SLOW  DISCHARGE. 


455.  The  Shock. — When  the  discharge  of  a  Leyden  jar 
takes  place  through  a  conductor  which  is  not  very  good, 
the  human  body,  for  instance,  it  produces  a  "  shock"  of 
more  or  less  severity. 

An  accidental  shock  led  to  the  invention  of  the  Leyden  jar.  A 
pupil  of  an  experimenter  in  Leyden  was  u  storing"  electricity  in  a 
bottle  of  water,  by  passing  a  rod  into  it  from  the  prime  conductor  of  a 
machine.  The  bottle  was  held  in  one  hand,  and  after  the  machine 


ELECTRICITY.  271 


had  been  in  operation  a  short  time  he  attempted  to  remove  the  rod 
from  the  water  with  the  other  hand,  when  he  was  surprised  and 
alarmed  by  receiving  a  shock.  The  news  of  this  shock  spread  with 
great  rapidity,  and  various  modifications  of  the  bottle  of  water  were 
soon  devised.  The  water  served  as  the  inside  coat  or  conductor,  and 
the  hand  of  the  operator  as  the  outside  coat.  Let  the  pupil  construct 
any  or  all  of  the  following  devices  and  take  shocks  from  them. 

456.  Various  Devices  for  giving  Shocks.— Experiment  175.— 

Fill  a  small  round  bottle  about  two-thirds  full  of  water.  Put  a  piece 
of  wire  or  a  nail  through  a  cork,  and  insert  the  cork  in  the  bottle. 
The  lower  end  of  the  wire  must  reach  into  the  water,  and  the  upper 
end  must  terminate  in  a  ball  or  ring.  Holding  the  jar  in  one  hand, 
present  the  ball  to  a  prime  conductor,  electrophorus,  excited  rod,  or 
even  a  gutta-percha  comb  drawn  through  the  hair.  After  the  ball 
has  taken  several  sparks,  touch  it  with  a  knuckle  of  the  free  hand. 

If  it  is  at  hand,  paste  tin-foil  as  a  coating  over  the  outside  of  the 
jar.  A  much  larger  condensing  surface  is  thus  obtained.  Or,  in- 
stead of  the  hand  or  tin-foil,  set  the  jar  in  a  vessel  partly  full  of 
water,  and  dip  a  finger  into  the  water  while  charging  and  discharging. 
•  Experiment  176. — Paste  a  sheet  of  tin-foil  on  each  side  of  a  pane 
of  glass.  The  foil  should  be  smaller  than  the  glass.  Support  the 
pane  thus  coated  horizontally  by  one  hand  placed  under  the  middle 
of  it.  Lay  a  coin  on  it.  Bring  the  top  coat,  with  the  coin  on  it, 
near  a  prime  conductor.  After  several  sparks  have  passed,  try  to 
pick  up  the  coin  with  one  hand  while  the  other  is  still  in  contact  with 
the  lower  coat. 

Experiment  177. — Let  one  pupil  hold  a  pane  of  glass  on  the  palm 
of  one  hand.  Let  a  second  pupil,  who  is  standing  on  a  stool  with 
glass  or  rubber  feet  (see  Exp.  180),  rest  his  open  hand  flat  on  the  glass, 
over  the  hand  of  the  other,  and  bring  a  knuckle  of  the  free  hand 
near  the  prime  conductor.  After  a  few  seconds,  let  them  bring  their 
free  hands  near  together. 

A  class  of  inventive  boys  or  girls  will  vary  these  experiments  in- 
definitely. The  shocks  given  by  either  of  these  devices,  or  by  a 
regular  Leyden  jar,  may  be  felt  by  several  at  once.  To  accomplish 
this,  let  all  form  a  circle  by  clasping  hands.  When  the  circle  is  com- 
plete, break  it  in  one  place,  and  let  the  two  persons  thus  separated 
touch,  one  the  outside  and  the  other  the  ball  of  the  charged  Leyden 
jar,  or  the  corresponding  parts  of  any  other  device. 

A  Leyden  jar  of  a  capacity  of  one  quart  will  furnish  a  shock  suffi- 
ciently severe  for  one  person,  though  two  or  three  times  the  amount 
of  surface  which  it  contains  might  be  discharged  through  the  human 
body  without  producing  permanent  injury.  A  large  number  of  per- 
sons may  take  the  discharge  of  a  larger  jar  without  injury. 

457.  The  Discharge  Instantaneous,— Experiment  178.— To 

prove  that  the  discharge  of  the  Leyden  jar  by  a  conducting  rod  (and 


272  NATURAL  PHILOSOPHY. 

therefore  presumably  through  the  human  system  also)  is  instantane- 
ous, set  a  wheel  to  rotating  so  rapidly  that  the  spokes  cannot  be  dis- 
tinguished. Darken  the  room,  and  discharge  a  Leyden  jar  near  the 
wheel.  The  separate  spokes  will  not  only  be  seen,  but  the  wheel  will 
appear  to  be  stationary. 

What  is  thus  true  of  the  spark  of  the  Leyden  jar  is 
true  of  the  electric  spark  under  any  circumstances.  A 
rapidly-rotating  carriage- wheel,  or  even  a  moving  cannon- 
ball,  illuminated  at  night  by  lightning,  appears  stationary. 

458.  Heat  and  Light  from  Electricity. — In  previous  chap- 
ters we  have  learned  that  resistance  to  motion  causes  the 
molecular  vibrations  which  produce  heat  and  light.  The 
same  effect  is  produced  by  resistance  to  the  free  passage  of 
electricity.  Passing  over  a  good  conductor,  electricity  pro- 
duces no  visible  effects.  The  particles  of  bad  conductors 
are  so  shaken  up  by  their  unsuccessful  attempts  to  stop  the 
flow  of  the  electric  charge  through  them  that  they  fre- 
quently develop,  first,  heat,  then  light.  The  ordinary  elec- 
tric spark  is  caused  by  the  heating  of  the  molecules  of  air 
and  "  dust"  in  the  path  of  the  discharge.  When  the  elec- 
tric spark  is  produced  in  any  other  gas,  the  color  of  the 
spark  is  characteristic  of  that  gas  in  a  state  of  incan- 
descence. 

It  is  a  well-known  fact  that  barns  and  other  buildings 
are  burned  by  lightning.  Lightning  is  ordinarily  due  to  a 
discharge  between  two  clouds  differently  electrified,  but  in 
cases  in  which  objects  on  the  earth  are  "  struck"  it  is  a 
discharge  between  a  cloud  and  the  earth.  Should  it  strike 
a  poor  conductor  of  comparatively  small  size  in  its  line 
of  connection  with  the  earth,  it  develops  heat,  sometimes 
enough  to  fire  the  object. 

The  following  experiments  exhibit  the  heating  power  of  the  elec- 
tric spark  on  a  smaller  scale. 

Experiment  179. — Present  a  very  shallow  metal  cup  containing  a 
spoonful  of  ether  or  carbon  bisulphide  to  the  prime  conductor  of  a 
machine.  The  spark  will  ignite  the  liquid. 

Experiment  180. — Support  a  dry  board  about  one  by  two  feet  on 
three  or  four  stout  tumblers,  bottles,  pieces  of  wax,  or  on  feet  shod 


ELECTRICITY. 


273 


with  india-rubber.  This  is  an  insulating  stool.  Stand  on  this  stool, 
and  take  in  one  hand  a  chain  or  wire  leading  from  the  prime  con- 
ductor. Take  in  the  other  a  cold,  dry  icicle. 
Presented  quickly  to  a  vessel  of  carbon  bisul- 
phide, or  to  an  ordinary  gas-burner,  the  bisul- 
phide or  the  gas  may  be  ignited.  This  is  pretty 
sure  to  succeed  best  if  the  gas-burner  is  used, 
and  turned  upside  down,  the  icicle  being  pre- 
sented from  below  (Fig.  267).  Any  water  that 
may  chance  to  form  will  then  run  back  on  the 
icicle  instead  of  collecting  on  the  end  in  a  drop, 
which  tends  to  dissipate  the  charge  and  prevent 
a  spark. 


Mixtures  of  oxygen  and  hydrogen,  gun- 
powder, gun-cotton,  and  other  explosives 
may  be  ignited  by  the  electric  spark.  To 
fire  gunpowder,  the  discharge  must  pass 
through  a  poor  conductor,  e.g.,  a  wet 
string,  before  reaching  the  metal  ball 
suspended  over  the  powder.  Otherwise, 
by  the  suddenness  of  the  discharge,  the 
powder  is  blown  away  and  not  ignited. 

459.  The   Insulating   Stool, — The  insulating   stool   affords   a 
means  of  endless  instruction  and  entertainment.    A  person  standing  on 
such  a  stool  may  be  charged  by  connection  with  the  prime  conductor  of 
a  machine,  or,  standing  near  a  conductor,  he  may  be  electrified  by  in- 
duction, or  by  presenting  a  knife-point  or  a  row  of  pins  to  a  prime  con- 
ductor, or  a  revolving  plate  or  cylinder,  or  excited  rod,  he  may  make 
a  prime  conductor  of  himself.     In  either  case  a  few  energetic  school- 
mates will  think  of  a  dozen  expedients  for  testing  his  electric  condition. 

460.  Mechanical    Effects   of   Electric  Discharge.— The 

electric  shock  is  sufficient  evidence  that  the  passage  of 
electricity  through  a  poor  conductor  produces  a  shaking 
of  the  body,  rather  different  from  the  molecular  vibrations 
which  produce  heat.  A  loose  block  of  wood  is  shaken  by 
having  a  Leyden  jar  discharged  through  it.  A  piece  of 
paper  placed  between  the  knob  of  a  Leyden  jar  and  the 
knob  of  the  discharger  is  pierced  by  the  discharge  of  the 
jar.  A  large  jar,  or  several  jars,  will  pierce  thick  card- 
board, leather,  and  even  glass. 


274  NATURAL  PHILOSOPHY. 

461.  The  Charge  on  the  Surface. — Delicate  experiments 
have  shown  that  the  charge  of  an  electrified  body  lies  wholly 
on  the  surface.     A  hollow  sphere  of  the  thinnest  metal  will 
contain  as  heavy  a  charge  as  a  solid  ball  of  the  same  size, 
and  so  with  a  conductor  of  any  external  shape. 

This  may  be  experimentally  proved  by  trying  the  inside  and  out- 
side of  a  hollow  charged  conductor  with  the  proof-plane  and  electro- 
scope. Faraday l  tried  the  experiment  on  a  much  larger  scale.  He 
built  a  box  of  wood  twelve  feet  in  each  dimension,  and  covered  it  over 
with  copper  wires  and  tin-foil.  This  was  connected  with  a  powerful 
machine;  and  then  (in  his  own  words)  UI  went  into  the  cube  and 
lived  in  it,  using  lighted  candles,  electrometers,  and  all  other  tests  of 
electrical  states.  I  could  not  find  the  least  influence  upon  them,  or 
indication  of  anything  particular  given  by  them,  though  all  the  time 
the  outside  of  the  cube  was  powerfully  charged,  and  large  sparks  and 
brushes  were  darting  off  from  every  part  of  its  outer  surface." 

So  persistently  does  the  charge  keep  to  the  outside  that 
if  a  charged  conductor  be  turned  inside  out  any  number 
of  times  without  discharging  it,  the  electricity  shifts  from 
one  surface  to  the  other,  and  is  always  found  on  that  sur- 
face which  for  the  time  being  is  outside.  Faraday  devised 
for  this  experiment  a  linen  bag,  kept  open  by  a  ring  at  the 
mouth  and  turned  either  way  by  silk  strings  made  fast  to 
the  bottom. 

462.  Electrical  Tension  on  Different  Parts  of  a  Surface. — 
As  has  been  intimated  before,  the  amount  of  electricity  on 
a  given  area  of  the  surface  of  a  charged  conductor,  or  the 
electrical  tension,  varies  unless  the  surface  is  a  sphere.     On 
a  sphere  the  tension  is  equal  at  all  points  of  the  surface ;  on 
a  cylinder  with  round  ends  it  is  greatest  at  the  extremities ; 
on  an  egg-shaped  body  it  is  greatest  at  the  smaller  end ; 

1  Michael  Faraday,  English,  1791-1867,— one  of  the  most  noted 
philosophers  of  this  century.  His  researches,  abundant  and  striking 
in  many  branches  of  chemistry  and  physics,  were  especially  so  in 
electricity  and  magnetism.  He  was  the  discoverer  of  the  present 
method  of  producing  the  current  for  electric  lights,  and  of  many 
other  facts  and  methods  of  interest. 


ELECTRICITY.  275 


on  a  round  disk  it  is  greatest  at  the  circumference ;  on  a 
square  disk  it  is  greatest  at  the  corners ;  and,  in  general, 
on  symmetrical  surfaces  it  is  greatest  at  the  parts  farthest 
removed  from  the  centre  of  gravity  of  the  surface.  Points 
or  sharp  edges  connected  with  a  surface,  wherever  situated, 
show  the  greatest  tension,  hence  electricity  escapes  easily 
from  them  (Art.  446). 

463.  Thunder-Storms, — Every  one  now  knows  that  light- 
ning and  thunder  are  due  to  electricity.  The  discovery  was 
made  by  Dr.  Franklin  but  little  more  than  one  hundred 
years  ago.  How  the  electricity  is  produced  in  the  air  we 
are  not  prepared  to  say  with  certainty,  but  the  friction  of 
masses  of  air  over  one  another,  and  between  the  air  and 
particles  of  moisture  and  snow,  and  the  evaporation  and 
condensation  constantly  going  on,  are  capable  of  develop- 
ing a  large  quantity  of  free  electricity.  But,  however 
developed,  the  free  electricity  is  there  at  all  times,  though 
we  are  sensible  of  its  presence  mainly  at  the  time  of  thun- 
der-showers. The  phenomena  attending  these  storms  may 
be  explained  by  the  principles  which  we  have  just  learned. 
When  a  large  number  of  molecules  of  atmospheric  moist- 
ure condense  and  coalesce  to  form  a  cloud,  the  body  of  the 
cloud  becomes  a  conductor,  and  all  the  electricity  which 
may  previously  have  been  in  the  space  now  occupied  by 
the  cloud  comes  to  the  surface  and  there  acquires  consider- 
able tension.  Different  conditions  give  one  cloud  a  charge 
of  positive  and  another  a  charge  of  negative.  It  is  plain 
that  a  discharge  would  take  place  between  these  clouds 
when  they  come  sufficiently  near  to  each  other.  Or  a 
cloud  heavily  charged  with  either  kind  of  electricity,  on 
coming  near  a  neutral  cloud,  would  electrify  it  by  induc- 
tion, and  a  discharge  might  take  place  between  the  sides 
next  to  each  other,  which  would  be  oppositely  electrified 
(Art.  441).  These  are  discharges  between  clouds.  When 
a  cloud  heavily  charged  with  electricity  comes  near  the 
earth,  it  attracts  the  opposite  kind  of  electricity  by  indue- 


276  NATURAL  PHILOSOPHY. 


tion,  and,  as  the  earth  has  a  large  store  to  draw  upon,  or  a 
large  surface  to  distribute  the  repelled  electricity  over,  the 
charge  becomes  very  intense.  In  fact,  we  have  a  vast 
Leyden  jar,  the  air  acting  as  insulator.  When  the  layer 
of  air  between  the  two  becomes  too  thin  to  resist  the  ten- 
sion of  the  opposing  kinds  of  electricity,  they  combine,  and 
we  say  the  lightning  came  to  the  earth.  High  objects  are 
most  likely  to  be  thus  "  struck,"  partly  because  the  electric 
tension  on  such  would  be  greatest,  and  partly  because  the 
insulating  air  between  the  two  charges  is  thinnest  over 
such  places.  The  sudden  motion  of  the  air  along  the  line 
of  the  lightning  discharge,  caused  by  its  displacement,  and 
also  by  its  expansion  and  contraction  on  account  of  the 
intense  heat,  is  the  probable  cause  of  thunder. 

464.  Lightning-Rods. — We  are  now  ready  to  understand 
the  eifect  of  the  lightning-rod.     If  the  charge  excited  in 
the  earth  by  the  electrified  cloud  finds  a  pointed  conductor 
extending  towards  the  cloud,  it  tends  to  flow  from  the  point 
to  the  cloud,  and  thus  the  electricity  of  the  cloud  becomes 
neutralized  by  the  quiet  discharge  from  the  point,  and  the 
flash  of  lightning  and  the  "  striking"  are  avoided.     The 
most   efficient   lightning-rods   are   those   furnished   with 
several  points.     Even  then  there  should  be  several  on  a 
large  building  to  render  it  comparatively  safe  against  the 
intense  charges  which  clouds  sometimes  carry. 

Lightning-rods  should  be  of  ample  size  and  good  metal.  Wrought- 
iron  rods  should  be  nearly  an  inch  in  diameter.  Copper  rods  may  be 
somewhat  smaller.  They  should  run  several  feet  into  the  ground,  and 
be  connected  with  buried  water-pipes  (if  they  are  large),  or  else  they 
should  terminate  in  several  branches  and  be  packed  in  coke,  which  is 
a  good  conductor. 

465.  Electricity  in  Rarefied  Air. — Though  the  air  in  its 
ordinary  state  is  a  non-conductor  of  electricity,  highly- 
rarefied  air  carries  a  charge  with  but  little  resistance.     The 
aurora  borealis,  which  is  sometimes  seen  in  our  latitude, 
and  more  frequently  in  the  far  north,  is  probably  due  to 


ELECTRICITY.  277 


electric   currents  in  the  higher  and  rarer  regions  of  the 
atmosphere. 

A  philosophical-instrument-maker  will  furnish  an  "aurora  tube," 
with  which  a  beautiful  experiment  may  be  performed.  The  tube  has 
a  pointed  metal  rod  sealed  into  the  upper  end,  and  the  lower  end  fits 
the  air-pump.  On  exhausting  the  air  and  connecting  the  rod  at  the 
top  with  the  prime  conductor  of  a  machine,  the  tube  is  filled  with 
beautiful  rosy  streams  of  light,  visible  in  a  dark  room.  The  electri- 
fied particles  of  air  remaining  in  the  tube,  and  which  produce  the 
light,  are  attracted  like  other  electrified  bodies,  and  the  streams  may 
be  diverted  towards  the  hand  placed  against  the  outside  of  the  tube. 
In  a  succeeding  section  the  subject  of  electric  currents  in  rarefied 
gases  will  be  more  fully  treated  (Art.  514). 

Exercises. — 1.  Two  boys  stand  on  different  insulating  stools,  and 
one  strokes  the  other  a  few  times  with  a  cat's  skin  :  what  will  be  the 
difference  in  their  condition,  and  how  may  it  be  shown  ? 

2.  A  girl  on  an  insulating  stool  presents  a  row  of  pins  to  the  prime 
conductor  of  an  electrical  machine  in  operation  :  what  is  her  electri- 
cal condition  ? 

3.  If  the  induction-cylinder  of  Experiment  164  be  touched  to  the 
prime  conductor  of  a  machine,  what  will  be  its  condition  after  being 
removed  ? 

4.  Let  the  pupil  draw  a  diagram  representing  three  insulated  con- 
ductors in  a  row,  but  not  touching,  that  at  one'end  connected  by  wire 
with  the  prime  conductor  and  that  at  the  other  end  with  the  negative 
conductor :  indicate  by  the  signs   -f-  and  —  the  condition  of  each 
end  of  the  middle  cylinder. 

5.  If  an  excited  rod  be  held  over  some  very  small  pith  balls  lying 
on  a  table  and  then  over  some  others  lying  on  a  pane  of  glass,  what 
difference  in  their  behavior  should  be  noticed  ? 

II.— CURRENT  ELECTRICITY. 

466.  Definition. — Electricity  in  the  condition  in  which  it 
was  treated  in  the  last  section  has  generally  been  called 
frictional  electricity,  from  the  fact  that  it  is  most  readily 
developed  by  friction.  But,  whether  developed  by  friction, 
by  induction,  or  by  any  other  method,  it  always  possesses 
great  intensity.  On  this  account  it  is  frequently  called  high 
tension  electricity.  But  one  of  its  most  striking  character- 
istics is  shown  by  its  remaining  for  a  long  time  on  an  in- 
sulated body  as  a  charge  after  the  source  of  excitement  has 
been  withdrawn.  On  this  account  it  is  called  static  elec- 
tricity, the  word  static  meaning  standing  or  resting. 

24 


278  NATURAL  PHILOSOPHY. 

In  strong  contrast  with  this  kind  of  electrical  excitement 
is  the  electricity  produced  by  a  battery  such  as  may  be  seen 
in  any  telegraph-office.  Electricity  thus  developed  "  flows" 
constantly  over  a  conductor  (generally  a  wire)  so  long  as 
it  is  properly  connected  with  the  battery,  but  as  soon  as 
this  connection  is  broken  all  sensible  evidence  of  electrical 
excitement  in  the  wire,  or  in  anything  which  may  have 
been  connected  with  it,  ceases.1  The  electricity  produces 
its  effect  while  flowing  as  a  current  through  the  wire.  On 
this  account  it  is  called  current  electricity.  The  word  cur- 
rent means  running.  In  honor  of  two  early  experimenters 
with  it,  current  electricity  is  frequently  called  galvanism? 
or  voltaic*  electricity,  or  the  voltaic  current.  "  Galvanic  bat- 
tery" and  "  voltaic  battery"  are  general  terms  applied  to  all 
forms  of  battery  producing  current  electricity. 

467.  Principle  of  the  Voltaic  Battery.— The  origin  of  the 
electric  current  produced  by  a  battery  is  chemical  action 
between  two  substances,  generally  an  acid  fluid  and  a 
metal. 

Experiment  181. — Put  into  any  convenient  small  glass  vessel  a 
mixture  of  1  part  of  sulphuric  acid  to  10  or  20  parts  of  water.  Dip  into 
this  a  strip  of  zinc  and  a  strip  of  copper.  A  copper  cent,  fastened  to  a 
wire,  answers  very  well  for  the  copper  strip.  Set  the  vessel  in  a  light 
place  and  examine  the  liquid  near  each  metal  strip.  Minute  bubbles 
may  be  seen  rising  from  the  sides  of  the  zinc,  but  none  from  the  cop- 
per. Touch  the  zinc  and  copper  together  above  the  surface  of  the 
liquid,  the  lower  parts  remaining  immersed.  Bubbles  will  begin  to 

1  This  is  not  strictly  correct  when  applied  to  conductors  of  enor- 
mous size,  such  as  an  ocean  telegraph-cable  several  thousand  miles 
long,  or  when  the  current  is  made  by  a  very  powerful  battery. 

2  Aloisio  Galvani,  Italian,  1737-1798,  Professor  of  Physiology  at 
Bologna,  discovered   that  a  piece  of  copper  and  a  piece  of  zinc  in 
contact  with  the  nerves  and  muscles  of  a  dead  frog,  and  with  each 
other,  give  rise  to  a  current  of  electricity. 

3  Alessandro  Volta,  Italian,  1745-1827,  discovered  that  any  two 
metals  in  contact,  and  in  situation  to  be  chemically  acted  on,  give 
currents  of  electricity.     He  was  the  inventor  of  Volta's  pile,  and  of 
the  simple  voltaic  or  galvanic  battery. 


ELECTRICITY. 


279 


rise  rapidly  from  the  copper  plate,  and  a  few  will  probably  continue 
to  rise  from  the  zinc.  Separate  the  metals,  and  the  bubbles  stop 
rising  from  the  copper  plate. 

These  bubbles  are  hydrogen  gas,  liberated  from  the  water 
(which  is  composed  of  oxygen  and  hydrogen)  by  the  chem- 
ical union  of  the  zinc  with  the  other  elements  of  the  acid 
fluid.  This  chemical  action  is  accompanied  by  the  develop- 
ment of  electricity,  which,  when  the  metals  are  in  contact, 
or  connected  by  a  wire,  takes  the  form  of  a  "  current" 
through  the  wire,  from  the  copper  to  the  zinc.  This  chem- 
ical action  and  electrical  excitement  are  inseparable,  one 
undoubtedly  dependent  on  the  other.  If  the  chemical  action 
is  stopped,  the  current  ceases;  and  if  the  current  is  stopped,  the 
chemical  action  ceases. 

468.  Pure  Zinc  needed, — The  continuous  rise  of  bubbles  from 
the  zinc  is  due  to  slight  traces  of  some  other  metals  as  impurity. 
The  particles  of  such  metals  being  in  contact  with  the  zinc,  a  num- 
ber of  small  "  local"  currents  are  established.     This  action  uses  up 
the  zinc  without  giving  any  compensation  in  the  way  of  a  current 
over  the  wire,  where,  only,  we  can  make  use  of  it.    A  pure  metal  by 
itself  is  not  dissolved  in  the  dilute  acid.     The  surface  of  the  zinc  is 
rendered   practically   pure  by 

coating  it  with  mercury.  Zinc 
so  coated  is  said  to  be  amalga- 
mated. 

Experiment  182. — To  amal- 
gamate zinc,  dip  it  into  dilute 
sulphuric  acid  for  an  instant, 
and  then  rub  it  or  slap  it  with 
a  little  muslin  bag  containing 
an  ounce  or  two  of  mercury. 
Make  it  shine  all  over,  and 
repeat  Experiment  181,  using 
the  amalgamated  zinc. 

469.  The  Simple  Voltaic 
Cell. — The  apparatus  em- 
ployed in  the  last  experi- 
ment is  essentially  a  vol- 
taic cell.     Fig.  268  shows  a  form  of  nicely-made  cell.     The 
arrows  show  the  direction  of  the  current  along  the  wire 


Fiu.  268. — VOLTAIC  CELL. 


280 


NATURAL   PHILOSOPHY 


M.  The  upper  extremities  of  the  plates,  or  of  the  wires 
attached  to  them,  are  the  poles,  or  electrodes.  The  positive 
and  negative  are  indicated  respectively  by  the  signs  -|- 
and  — .  We  may  conceive  of  electricity  being  propagated 
along  the  wire  from  the  negative  as  well  as  from  the  posi- 
tive electrode,  but  the  direction  on  the  wire  from  the  positive 
to  the  negative  is  spoken  of  as  the  direction  of  the  current. 

The  wire,  the  plates,  and  the  liquid  between  the  plates 
constitute  the  circuit.     If  all  parts  of  the  circuit  are  con- 
ductors of  electricity,  the  circuit  is  said  to  be  closed.    When 
any  break  exists  in  the  circuit,  as  would  be  the  case  if  the 
wire  were  disconnected  from  one  plate,  or  if  either  plate 
were  taken  out  of  the  liquid,  the  circuit  is  said  to  be  open. 
Many  combinations  are  used  in  the  construction  of  different  kinds 
of   batteries.      Instead   of  dilute  sul- 
phuric  acid,  a   saturated    solution  of 
sulphate  of  copper — i.e.,  blue  vitriol,  or 
"blue-stone" — may  be  used.     This  is 
the  gravity,  or  Callaud  (kal-lo')  cell, 
shown  in  Fig.  269.     It  is  the  common 
"  local  battery"  in  way-stations  on  tele- 
graph lines.     Gas  carbon  may  be  used 
instead  of  copper  for  the  positive  elec- 
trode.   Gas  carbon  and  zinc,  in  an  acid 
solution  of  bichromate  of  potassium, 
forms  a  very  convenient  and  effective 
battery    for     experimental     purposes. 
This   is  called   the  "one-fluid  bichro- 
mate battery."     A  dozen  other  single- 
fluid  cells  might  be  mentioned.     Zinc 

is  almost  universally  used  as  the  positive  metal,— i.e.,  the  metal  acted 
on  by  the  acid. 

470.  Two-Fluid  Cells.— In  most  single-fluid  cells  the 
hydrogen  retards  the  action.  With  two  fluids  this  may  be 
obviated.  The  most  powerful  of  the  two-fluid  batteries  is 
Grove's.  The  zinc  plate,  in  the  form  of  a  hollow  cylinder,  or 
something  equivalent,  is  immersed  in  dilute  sulphuric  acid 
contained  in  a  glass  vessel.  A  vessel  of  porous  earthen- 


FIG.  269. — GRAVITY,  OR  CALLAUD 
CELL. 


ELECTRICITY.  28l 


ware,  filled  with  strong  nitric  acid,  is  set  in  the  hollow 
zinc,  and  is,  of  course,  surrounded  by  the  dilute  sulphuric 
acid.  A  strip  of  platinum,  immersed  in  the  nitric  acid, 
completes  the  cell.  The  nitric  acid  supplies  oxygen,  which 
unites  with  and  removes  the  hydrogen  that  would  other- 
wise surround  the  platinum.  Platinum  is  used  because  it 
is  not  dissolved  by  nitric  acid.  The  porous  earthenware 
cup  becomes  soaked  with  the  acids,  and  thus  conducts  the 
current  of  electricity,  but  it  does  not  permit  of  much  mix- 
ing of  the  liquids.  Bunsen's  battery  uses  gas  carbon  in- 
stead of  platinum.  (See  Figs.  272  and  273.) 

471.  Batteries  of  Several  Cells.— The  term  "  battery"  has 
been  unavoidably  used  several  times  in  the  last  few  pages. 
The  different  arrangements  which  have  been  described  as 
producing  the  voltaic  current  are  properly  cells.     A  cell  of 
a  given  construction  gives  a  current  of  a  definite  strength, 
or,  rather,  of  a  definite  electro-motive  force.     In  order  to  ob- 
tain more  electro-motive  force  than  one  cell  will  give,  we 
connect  several  cells  together  by  means  of  wires.     Such  an 
arrangement  is  properly  a  voltaic  battery.     Fig.  272  shows 
a  Bunsen's  battery  of  two  cells,  and  Fig.  273  one  of  four  cells. 

It  will  be  seen  in  Fig.  273  that  the  zinc  of  the  right-hand 
cell  is  connected  with  the  carbon  of  the  second  cell,  the  zinc 
of  the  second  with  the  carbon  of  the  third,  and  so  on  through 
the  battery.  When  the  first  zinc  and  the  last  carbon  are 
connected,  the  circuit  is  closed  and  the  current  flows. 

472.  Characteristics  of  Current  Electricity. — In  Art.  466 
current  electricity  is  so  called  because  its  chief  characteristic 
is  that  it  does  its  work  and  makes  itself  known  only  as  it 
flows  through  a  conductor.     This  is  true  of  currents  from 
all  ordinary  batteries.     With  an  enormous  battery  of  hun- 
dreds or  thousands  of  cells  a  current  may  be  obtained 
which  has  an  appreciable  amount  of  tension,  or  tendency  to 
escape ;  but  even  this  is  very  low  compared  with  the  ten- 
sion of  the  electricity  on  the  prime  conductor  of  a  working 
electrical  machine.     The  difference  between  frictional  and 

24* 


282 


NATURAL  PHILOSOPHY. 


voltaic  electricity  may  therefore  be  considered  a  difference 
in  the  intensity  of  the  eleclrical  excitement,  and  voltaic 
electricity  may  properly  be  called  electricity  of  low  tension. 
The  quantity  of  electricity  developed  by  an  ordinary  bat- 
tery is  very  much  greater  than  that  developed  in  the  same 
time  by  an  ordinary,  or  even  a  very  large,  electrical  ma- 
chine. The  constancy  and  rapidity  of  the  current  take  a 
large  quantity  through  a  conducting  wire  in  a  given  time. 
On  good  conductors  the  rate  of  an  electric  current  has  been 
measured  at  more  than  200,000  miles  per  second.  Electro- 
motive force  is  the  force  with  which  a  current  is  urged  for- 
ward, and  is  shown  by  the  ability  of  a  current  or  a  charge 
to  jump  through  an  insulator.  The  charge  of  a  small 
electrophorus  lid  will  jump  one-fourth  of  an  inch  through 
the  air.  The  current  from  a  thousand  Bunsen  cells  will 
produce  a  spark  scarcely  y^nr  of  an  inch  in  length.  The 
electro-motive  force  of  current  electricity  is  very  small. 
A  number  of  cells  connected,  as  shown  in  Fig.  273,  increase 
the  electro-motive  force  in  the  direct  ratio  of  the  number 
of  cells  employed.  A  battery  so  connected  is  said  to  be 
connected  for  intensity  of  current,  or  connected  in  series. 


FIG.  270. — BATTERY  CONNECTED  "  SIDE  BY  SIDE." 

When  a  larger  quantity  of  electricity  is  wanted  than  one 
cell  will  produce,  several  cells  are  connected  side  by  side, 
as  shown  in  Fig.  270, — i.e.,  the  zinc  plates  are  all  connected 
with  one  wire,  and  the  carbon  plates  with  another. 


ELECTRICITY. 


283 


473.  Resistance, — The  electric  current  encounters  some 
resistance  in  all  parts  of  the  circuit.     The  resistance  in  the 
liquid  of  the  battery  is  very  great  compared  with  that  in 
the  same  length  of  connecting  wire.     In  a  wire  of  given 
material  the  resistance  is  directly  proportional  to  the  length 
of  the  wire,  and  inversely  proportional  to  the  area  of  its 
cross-section.1    Different  conductors  offer  different  amounts 
of  resistance.     When  the  resistance  is  considerable,  an  ap- 
preciable amount  of  heat  results.     Thin  wires  of  platinum 
and  thin   strips  of  carbon  are  readily  rendered  white-hot 
by  the  passage  of  the  current.     If  a  copper  or  iron  con- 
ducting wire  from  a  battery  be  cut  in  one  or  more  places, 
and  pieces  of  thin  platinum  wire  be  stretched  across  the 
breaks  thus  formed,  they  become  white-hot  on  the  passage 
of  a  moderately-strong  current,  and  will  ignite  illuminating 
gas,  gunpowder,  or  any  similar  substance  in  which  they 
may  be  placed.     Such  arrangements  are 

very  extensively  used  in  lighting  the  gas 
in  high  buildings  and  in  blasting  in  mines. 
Platinum  offers  much  more  resistance  than 
copper,  and  the  thin  wire  more  than  a 
thicker  one  would.  The  thicker  tele- 
graph-wires are,  the  better  they  will  per- 
form their  work. 

474.  The  Edison  Lamp. — The  Edison  elec- 
tric lamp  consists  of  a  small  ribbon  of  paper-char- 
coal in  the  form  of  a  horseshoe,  placed  between 
metal  tips  in  a  glass  globe  from  which  the  air  has 
been  exhausted.     Fig.  271  shows  the  general  ap- 
pearance of  the  lamp.     A  current  being  passed  through  from  one  of 
the  wire  ends  to  the  other,  the  carbon  is  intensely  heated  on  account 
of  its  resistance.     As  no  air  is  present,  it  cannot  burn  away,  and  so 

1  For  instance,  a  copper  wire  200  feet  long  offers  twice  as  much 
resistance  as  one  of  the  same  diameter  100  feet  long.  A  wire  of  a 
given  length  and  -fa  of  an  inch  in  diameter  offers  4  times  as  much  re- 
sistance as  a  wire  of  the  same  length  and  TJ^  of  an  inch  in  diameter, 

*•«•»  (A)*:  (A)1- 


284  NATURAL  PHILOSOPHY. 

will  give  a  continuous  light  for  many  weeks  or  months.  Other 
incandescent  electric  lamps  are  in  use,  some  of  which  use  platinum 
instead  of  carbon. 

475.  Division  of  Current. — If  two  conductors  extend  be- 
tween the  plates  of  a  battery,  or  are  so  introduced  into  a 
circuit  that  the  current  may  take  either,  a  part  of  it  takes 
each  route,  and  the  amounts  are  in  the  inverse  ratio  of  the 
resistances  of  the  conductors.     If,  for  instance,  two  copper 
wires  of  equal  length  and  equal  thickness  extend  between 
two  points  in  a  circuit,  half  of  the  current  will  follow  each. 
If  two  points  in  a  circuit  be  connected  by  two  copper 
wires,  one  of  which  is  ^  of  an  inch  in  diameter  and  the 
other  -^  of  an  inch,  and  both  of  the  same  length,  the 
larger  wire  will  carry  £  of  the  circuit,  and  the  smaller  J. 
In  this  way  currents  are  frequently  divided  for  purposes  of 
electric  lighting,  duplex  telegraphing,  etc.     So  a  current 
may  be  divided  into  any  number  of  parts. 

476.  The  Ohm. — The  unit  of  resistance  is  the  ohm.     This 
is  used  in  designating  the  amount  of  electricity  required 
to   produce  a  given   effect   in   electric   lamps,   telegraph- 
"  sounders,"  etc.     It  is  nearly  the  resistance  offered  by  666 
feet  of  copper  wire  ^  of  an  inch  in  diameter.     The  resist- 
ance of  1332  feet  of  copper  wire  ^  of  an  inch  thick  would 
be  32  ohms  (2  X  42). 

477.  Resistance  and  Work. — The  amount  of  work  done  by 
a  given  current  in  any  part  of  its  circuit  is  directly  proportional 
to  the  resistance  of  that  part  of  the  circuit. 

This  applies  to  the  amount  of  light  or  heat  developed  in 
the  conducting  wire,  the  strength  of  magnetic  attraction 
caused  by  electric  currents,  etc. 

478.  The  law  of  the  conservation  of  energy  is  forcibly  illustrated 
by  the  heating  and  lighting  eifects  of  the  electric  current.     The 
burning  of  the  zinc  before  a  blow-pipe,  or  in  a  furnace,  would  pro- 
duce both  heat  and  light.     When  it  is  consumed  in  a  battery  the 
same  amount  of  energy  is  given  out,  but  in  the  form  of  an  electric 
current,  which  in  turn  is  converted  into  heat  and  light,  and  which, 
as  we  shall  presently  learn,  is  far  more  effective  than  ordinary  fric- 
tional  electricity  in  producing  motion. 


ELECTRICITY. 


285 


479.  Electrolysis. — In  the  production  of  the  electric  cur- 
rent the  water  of  the  battery  is  separated  into  oxygen  and 
hydrogen.  If  the  conducting  wires  be  immersed  in  another 
vessel  of  water,  so  that  it  will  form  part  of  the  circuit,  this 
water  will  also  be  decomposed,  oxygen  being  liberated 
from  the  positive  electrode  and  hydrogen  from  the  nega- 
tive. Fig.  272  shows  the  method  of  illustrating  this.  As 


FIG.  272. — ELECTROLYSIS  OP  WATER. 

water  is  composed  of  two  volumes  of  hydrogen  to  one  of 
oxygen,  one  tube  will  collect  gas  twice  as  fast  as  the  other. 
Electro-plating. — The  galvanic  battery  decomposes  not  only 
water,  but  solutions  of  very  many  salts  of  the  different  metals.  The 
metal  of  the  salt  separates  in  a  pure  state.  The  metals  are  generally 
positive  with  reference  to  the  other  ingredients  of  a  salt,  and  therefore 
separate  at  the  negative  electrode.  If  we  wish  something  coated  or 
"  plated"  with  silver,  gold,  or  nickel,  it  is  made  the  negative  electrode 
of  a  battery  by  attaching  it  to  the  wire  from  the  zinc.  It  is  then  dipped 
into  a  proper  solution  of  the  metal  which  we  wish  to  plate  with.  On 
dipping  into  the  same  liquid  a  plate  attached  to  the  positive  wire  of 
the  battery  the  circuit  will  be  closed  through  the  solution,  the  salt  will 
be  decomposed,  and  the  metal  deposited  on  the  negative  electrode. 
Fig.  273  shows  a  silver-plating  tank  in  operation.  The  vessels  and 
other  articles  which  are  being  plated  are  all  suspended  from  the  rods 
which  are  connected  with  the  zinc  electrode  of  the  battery.  The  large 
square  plates  suspended  from  the  positive  electrode  are  pure  silver, 


286 


NATURAL  PHILOSOPHY. 


which  is  dissolved  as  the  process  goes  on  and  keeps  the  solution  of  a 
uniform  strength. 

Any  boy  or  girl,  with  very  little  outlay,  may  find  instructive  enter- 
tainment in  electro-plating.    The  apparatus  here  figured  may  be  of 


FIG.  273. — ELECTRO-PLATING,  WITH  BATTERY  OF  FOUR  BUNSEN  CELLS. 

very  much  smaller  dimensions.  The  battery  may  be  home-made,  a 
tumbler  will  hold  the  plating-solution,  and  a  brass  watch-chain  or 
hook,  or  a  copper  cent,  may  be  plated.  In  fact, 
plating  may  be  done  in  the  battery,  and  that  may 
be  easily  constructed. 

Experiment  183. — Put  a  small  silver  coin  into  a 
dish  and  pour  over  it  a  few  teaspoonfuls  of  nitric  acid. 
(It  should  be  out  of  doors  or  in  a  fireplace,  as  the 
fumes  are  hurtful.)     If  the  acid  is  strong,  put  in  as 
much,  or  twice  as  much,  water.    Heat  the  dish  mod- 
erately.    The  coin  will  dissolve  rapidly.    When  the 
coin  has  disappeared,  pour  the  solution  into  a  glass 
vessel.    Add  some  weak  u  muriatic"  acid,  or  a  strong 
FIG  274— SILVER-    solution  of  salt  in  water,  as  long  as  it  continues  to 
PLATING  A  COIN,     form    white    "  curds"    in    the   liquid.     These  white 
curds  are  chloride  of  silver.     They  will  settle  to  the 
bottom  of  the  vessel.    Pour  off  the  blue  liquid,  or  most  of  it.    Fill  up 
the  vessel  with  water,  and  pour  off  several  times.     This  is  to  remove 
the  copper  with  which  the  silver  of  the  coin  was  alloyed.     It  is  blue 
in  the  solution,  and  when  the  blue  color  disappears  the  chloride  of 
silver  is  washed  enough.     It  will  be  necessary  now  to  have  about  an 
ounce  of  cyanide  of  potassium,  a  very  poisonous  salt,  used  to  wash 


ELECTRICITY.  287 


out  stains  of  indelible  ink.  Dissolve  this  in  water,  and  add  it  to  the 
chloride  of  silver,  stirring  it  round  till  the  white  curds  are  all  dis- 
solved. Make  this  quite  weak  by  the  addition  of  water.  A  dime 
will  make  a  half-pint  of  liquid  strong  enough  for  our  present  purpose. 
Fill  a  porous  battery  cup  with  this,  or,  if  that  is  not  at  hand,  a  flower- 
pot with  the  hole  stopped  with  plaster  or  putty,  or,  for  a  small  quan- 
tity, the  "  bowl"  of  a  tobacco-pipe  with  a  plug  in  the  broken-off  stem. 
Set  this  in  any  convenient  glass  vessel,  and  till  that  with  dilute  sul- 
phuric acid  to  the  level  of  the  silver  solution.  Put  a  piece  of  zinc 
in  the  outer  vessel,  and  suspend  from  it  by  a  wire  a  small  clean  article 
to  be  plated.  Take  it  out  and  rub  it  with  a  cloth  after  a  minute. 
Eepeat  several  times,  each  time  leaving  it  in  longer.  In  ten  minutes 
there  will  be  a  very  good  plating,  and  in  an  hour  or  more,  depending 
on  the  strength  of  the  current,  a  really  thick  plating. 

480.  Deposit  always  on  the  Negative  Plate. — It  will  be 
noticed  that  in  the  above  experiment  the  article  to  be 
plated  takes  the  place  of  the  copper  plate,  while  in  the 
methods  given  in  which  the  battery  and  the  plating  solu- 
tions are  separate  the  article  to  be  plated  is  fastened  to  the 
wire  from  the  zinc  plate.     This  is  because  in  the  battery  the 
copper  is  the  negative  plate.     The  negative  plate  is  that 
towards  which  the  positive  current  flows.    If  the  circuit  be 
opened  at  any  place,  that  end  of  the  break  from  which  the 
current  flows  is  the  positive,  and  that  towards  which  it  flows 
is  the  negative,  electrode.     In  determining  where  to  place 
an  article  to  be  plated,  remember  that  the  metal  is  carried 
with  the  current  in  the  plating  solution,  and  that  the  current 
flows  around  continuously  from  copper  to  zinc  in  the  wire, 
and  from  zinc  to  copper  in  the  battery. 

Many  interesting  variations  of  the  above  plating  experiment  may 
be  tried.  Any  ordinary  soluble  salt  is  decomposed  by  the  voltaic 
current,  the  metal  going  with  the  current  to  the  nearest  electrode. 

481.  Secondary  Batteries. — We  have  seen  that  the  cur- 
rent from  a  battery  has  the  power  of  separating  many 
compounds  into  their  constituent  parts.     The  reuniting  of 
substances  thus  separated  will,  under  proper  conditions, 
give  rise  to  a  voltaic  current  opposite  in  direction  to  the 
current  which  caused  the  decomposition.   This  fact  is  made 
use  of  in  the  construction  of  what  are  now  (1883)  just 
coming  into  use  under  the  name  of  secondary  batteries. 


288  NATURAL   PHILOSOPHY. 

Probably  the  most  successful  of  the  secondary  batteries  is  Faure's 
(for),  or  some-  one  of  the  very  numerous  modifications  of  it.  The 
principle  may  be  understood  from  a  description  of  the  original  form, 
devised  by  Faure.  It  consists  of  two  large  plates  of  very  thin  sheet- 
lead,  each  coated  with  a  layer  of  minium  (red  oxide  of  lead),  and 
rolled  together  into  a  spiral  like  a  roll  of  carpet.  The  sheets  are  kept 
separated  by  rolling  in  with  them  soft  paper  saturated  with  weak  acid. 
One  of  these  sheets  is  connected  with  each  of  the  wires  from  a  bat- 
tery. Oxygen  from  the  weak  acid  is  liberated  on  the  surface  of  the 
lead  plate  which  forms  the  positive  electrode,  and  hydrogen  on  the 
surface  of  that  which  forms  the  negative  electrode.  The  oxygen 
unites  with  the  coating  of  red  lead  on  the  positive  sheet,  converting 
it  into  a  higher  oxide  of  lead.  The  hydrogen  unites  with  the  oxygen 
of  the  red  lead  coating  on  the  negative  sheet,  and  forms  water,  re- 
ducing the  oxide  of  lead  to  pure  lead  in  a  very  fine  state  of  subdi- 
vision. When  all  the  red  lead  on  one  sheet  has  been  converted 
into  the  higher  oxide,  and  all  that  on  the  other  has  been  reduced  to 
the  condition  of  metallic  lead,  the  secondary  battery  is  said  to  be 
"charged."  If,  now,  the  wires  are  disconnected  from  the  charging 
battery  and  brought  into  contact  with  each  other,  a  current  will  be 
found  to  pass  through  them,  and,  as  said  before,  it  flows  backward 
with  reference  to  the  direction  of  the  primary  current,  or  from  the 
-oxidized  to  the  deoxidized  plate. 

482.  Energy  of  Secondary  Battery. — The  total  amount 
of  energy  given  out  in  the  discharging  of  a  secondary  bat- 
tery is,  of  course,  equal  to  that  consumed  in  charging  it, 
and  in  practice  this  may  nearly  all  be  made  available.  The 
total  "  quantity"  of  an  electric  current,  or  of  the  energy  of 
a  given  current,  is  equal  to  the  amount  for  any  unit  of 
time  multiplied  by  the  time  during  which  the  current  flows. 
A  secondary  battery  may  be  charged  by  a  small  battery 
working  for  a  considerable  length  of  time,  and  may  be  dis- 
charged in  a  powerful  current  flowing  a  proportionately 
short  time.  This  feature  renders  it  admirably  adapted  to 
electric  lighting,  or  to  the  driving  of  electric  motors,  where 
such  use  is  needed  for  but  a  small  part^of  each  day.  The 
secondary  battery  is  also  very  much  lighter  than  a  primary 
battery  required  to  give  a  current  of  equal  intensity.  It 
is  thus  adapted  to  use  where  the  size  and  weight  of  a  large 


ELECTRICITY.  289 


battery  are  an  objection.  It  has  already  been  applied  to 
driving  road-carriages  and  to  lighting  steamships  and  rail- 
way-cars. 

III.— ELECTRO-MAGNETISM. 

483.  Oersted's  Discovery.— About  the  year  1820,  Hans 
Christian  Oersted  (ur'sted),  Professor  of  Physics  at  the 
University  of  Copenhagen,  discovered  that  a  wire  through 
which  a  voltaic  current  is  flowing  has  the  power  of  de- 
flecting a  magnetic  needle  out  of  the  meridian.     This  dis- 
covery at   once  established  the  connection  between  elec- 
tricity and  magnetism,  and  laid  the    foundation   for  the 
many  useful  applications   of   "  electro-magnetism"  which 
we  now  see  all  about  us.     Oersted  also  discovered  that  the 
conducting  wire  of  a  battery  is  magnetic  while  the  current 
is  passing. 

484.  Direction  of  Deflection. — The  direction  in  which  a 
needle  is  deflected  by  ~*^ 

the     voltaic     current    -  < — rl|Sl + 

may  be  readily  re- 
membered by  the  fol- 
lowing rule : 

Consider  the  de- 
flecting force  to  rotate 
around  the  conduct- 
ing wire  as  the  thread 

Winds  around  a  SCreW,        FlG.  275. -SHOWING  DIRKCTION  OF  NEEDLE'S  DE- 

moving  from  the  head 

towards  the  point  of  the  screw, — that  is,  rotating  as  the 
hands  of  a  watch  turn.  When  the  current  is  passed  near 
a  magnetic  needle,  and  parallel  with  it,  the  north-pointing 
end  of  the  needle  is  turned  from  its  position  in  the  direction 
of  the  action  of  such  a  force,  whether  eastward  or  west- 
ward, or  upward  or  downward. 

For  instance,  suppose  a  current  pass  on  a  wire  parallel 
to  a  needle,  from  the  north  to  the  south,  if  it  pass  above 
N        t  25 


290 


NATURAL  PHILOSOPHY. 


the  needle,  the  north-pointing  pole  will  be  turned  east- 
ward ;  if  it  pass  beneath,  the  same  pole  will  be  turned 
westward ;  if  at  the  same  level  on  the  right-hand  side,  the 
north  pole  will  be  raised ;  if  on  the  left-hand  side,  it  will 
be  depressed. 

In  Fig.  275  the  arrow-head,  as  well  as  the  +  and  — 
signs,  indicates  the  direction  in  which  the  current  flows 
over  a  wire,  and  the  arrows  on  the  wheel  show  the  direc- 
tion of  rotation  of  the  magnetic  force.  In  whatever  posi- 
tion the  wire  is  held,  imagine  the  circumference  of  this 
wheel  to  strike  the  north  end  of  the  magnet  and  carry 
it  in  the  direction  of  its  own  motion. 

485.  The  Amount  of  Deflection  of  a  given  needle  depends 
on  the  total  effective  strength  of  the  current.  A  given  cur- 
rent may  multiply  its  effect  on  the  needle  by  passing  several 
times.  If  one  current  pass  above  a  needle  from  north  to 
south,  and  another  pass  beneath  it  from  south  to  north, 
the  two  currents  will  tend  to  deflect  the  needle  in  the 
same  direction,  and  the  effect  will  be  a  double  deflecting 
force.  The  same  result  is  obtained  when  the  wire  is  bent 
so  that  the  same  current  may  pass  in  one  direction  above 
the  needle,  and  in  the  other  direction 
under  it.  The  result  is  intensified  by  so 
coiling  the  wire  as  to  make  the  current 
pass  many  times  around  the  needle. 
This  principle  is  made  use  of  in  the  con- 
struction of  the  galvanometer,  or  instru- 
ment for  detecting  and  measuring  the 
galvanic  current. 

486.  Galvanometer.— Fig.  276  repre- 
sents a  common  form  of  galvanometer. 
It  has  a  double,  or  astatic  needle, — i.e., 
two  magnetic  needles  so  arranged  that 
they  neutralize  each  other's  tendency  to  stand  north-and- 
south,— suspended  by  a  thread  of  "unspun"  silk.  The 
graduated  circle  which  lies  on  the  coil  of  wire,  and  just 


FIG.  276.— GALVANOME- 
TER. 


ELECTRICITY.  291 


under  the  uppermost  needle,  indicates  the  amount  of  deflec- 
tion. 

487.  The  Electro-Magnet. — The  galvanometer  needle  is 
never  deflected  more  than  90  degrees,  or  till  it  stands  at 
right  angles  to  the  direction  of  the  electric  current.     A 
comparatively  feeble  current  will  turn  a  needle  nearly  at 
right  angles  to  its  course,  indicating  that  the  natural  posi- 
tion of  magnets  is  across  the  direction  of  electric  currents. 
Not  only  do  currents  tend  to  turn  magnets  into  this  direc- 
tion, but  they  magnetize  iron  or  steel  bars  near  which  they 
pass.   A  magnet  formed  by  passing  a  voltaic  current  across 
a  bar  of  iron  is  called  an  electro-magnet.     It  is  magnetic  only 
while  the  current  passes. 

488.  The  Helix. — A  current  crossing  an  iron  bar  only 
once  makes  a  very  feeble  magnet  of  it.     If  the  conducting 
wire  be  covered  with  an  insulating  cover  of  wax,  india- 
rubber,  silk,  or  even  cotton,  it  may  be  wound  many  times 
around  a  bar,  as  cotton  is  wound  on  a  spool.     As  many 
currents  multiply  the   effect  of  one,  there  is   scarcely  a 
limit  to  the  power  of  electro-magnets  thus  made.     Fig. 
277  shows  a  horseshoe  electro-magnet.     A  layer  of  wire 
wound  from  end  to  end  or  over  a  considerable  part  of  the 
length  of  a  bar  is  called  a  helix.     Several  layers,  such  as 
are  shown  on  each  arm  of  the  horseshoe  in  the  figure,  con- 
stitute a  coil. 

Experiment  184. — Procure  of  a  dealer  from  two  to  four  ounces  of 
very  fine  covered  copper  wire.  Wind  it  neatly  around  an  iron  bar 
as  large  as  an  ordinary  lead-pencil,  making  several  layers.  Connect 
the  free  ends  of  the  wire  with  any  simple  battery,  and  experiment 
with  the  electro-magnet  thus  formed.  Dip  it  into  nails,  and,  when 
it  is  loaded,  break  the  circuit.  Notice  that  some  of  the  nails  in- 
cline to  stay  on  after  the  current  is  stopped.  This  is  on  account  of 
the  residual  magnetism  which  iron  is  apt  to  exhibit  after  having  been 
once  magnetized.  Try  the  poles  of  the  electro-magnet  with  a  mag- 
netic needle,  and  notice  the  direction  of  winding  of  the  coil  of  wire 
as  looked  at  from  each  end.  Refer  to  rule  for  deflection  of  needle 
by  the  electric  current,  and  notice  that  the  same  rule  holds  here. 

As  electro-magnets  are  much  more  powerful  than  steel  magnets, 
they  are  mostly  used  in  magnetizing  steel  bars.  Fig.  278  shows  the 


292 


-    NATURAL   PHILOSOPHY. 


method  of  operation.     Of  course,  reference  to  the  direction  of  wind- 
ing indicates  the  respective  poles  of  the  electro-magnet. 


FIG.  277.— ELECTHO-MAGNET. 


489.  The  Helix  a  Magnet, — A  helix,  or  coil  carrying  a 
voltaic  current,  not  only  communicates  magnetic  properties 


FIG.  278.— MAGNETIZING  STEEL  BAR. 


to  the  bar  of  iron  in  the  middle,  or  "  core,"  but  is  itself  a 
magnet.     It  attracts  iron,  is  attracted  and  repelled  at  the 


ELECTRICITY.  293 


different  ends  by  the  poles  of  a  steel  magnet,  and,  if  prop- 
erly suspended,  arranges  itself  in  the  magnetic  meridian, 
the  hollow  centre  taking  the  north-and-south  direction.  If 
a  strong  steel  magnet  be  placed  directly  under  a  helix  sus- 
pended horizontally,  the  helix  assumes  the  direction  of  the 
length  of  the  magnet,  the  convolutions  of  the  wire  being 
across  its  length.  This  shows  a  mutual  action  between 
electric  currents  and  magnets,  and  that  they  are  naturally 
at  right* angles  to  each  other. 

490.  Electric  Currents  in  the  Earth.— The  north-and-south 

tendency  of  magnets  may  be  due  to  electric  currents  flowing  westward 
around  the  earth.  In  cases  of  unusual  fluctuation  of  the  compass, 
electric  currents  have  frequently  been  detected,  in  such  direction  as 
they  should  flow,  to  account  for  some  of  the  observed  phenomena. 
The  existence  of  currents  to  account  for  all  the  ordinary  phenomena 
of  the  magnetic  needle  is  not  established,  but  there  are  strong  reasons 
for  believing  that  they  do  exist. 

491.  Magnetic  Storms. — Telegraph-operators  frequently  report 
electrical  or  "  magnetic  storms,"  which  are  sometimes  of  considerable 
extent  and  cause  them  much  inconvenience.     They  are  not  neces- 
sarily accompanied  by  wind,  rain,  snow,  or  any  other  of  the  phenom- 
ena ordinarily  included  in  the  term  "storm,"  but  are  simply  dis- 
turbances in  the  electrical  or  magnetic  condition  of  the  earth  and  the 
air.     Magnetic  needles  move  backward  and  forward  through  several 
degrees,  telegraph-wires  refuse  to  carry  the  battery  currents  with  any 
regularity,  and  fine  displays  of  aurora  borealis  are  witnessed.     The 
aurora  may  not  be  seen  where  the  disturbances  are  felt,  but  it  is  sure 
to  be  visible  somewhere  within  a  few  thousand  miles  of  the  centre  of 
greatest  disturbance. 

As  illustrations  of  the  effect  of  such  storms,  we  quote  from  Chicago 
dispatches  an  account  of  the  effect  there  of  one  which  occurred  in  the 
autumn  of  1882 :  "  The  storm  seemed  to  go  in  successive  negative 
and  positive  waves,  alternately  neutralizing  the  currents  on  the  tele- 
graph lines,  or  increasing  their  intensity  to  such  a  degree  as  to  burn 
things  up.  The  '  switch-board'  at  Chicago  was  on  fire  a  dozen  times, 
and  half  a  dozen  keys  of  instruments  were  melted.  The  atmospheric 
electricity  on  one  of  the  country  wires  had  such  power  as  to  suffice 
to  keep  an  electric  lamp  burning.  Fully  two-thirds  of  the  sky  is 
ablaze  to-night  with  auroral  light  of  many  colors,  a  rare  phenomenon 
in  this  region."  At  Nashville,  during  the  same  storm,  the  telegraph 

25* 


294  NATURAL  PHILOSOPHY. 

lines  "  were  worked  at  intervals  solely  by  the  auroral  current.  The 
needle  in  the  galvanometer  oscillated  in  a  most  eccentric  manner, 
varying  as  much  as  80  degrees."  This  storm  was  wide-spread,  ex- 
tending over  all  the  northern  half  of  the  United  States  and  north 
and  east  as  far  as  telegraph  lines  extend.  A  dispatch  was  sent  from 
Bangor,  Maine,  to  North  Sydney,  Cape  Breton,  a  distance  of  700 
miles,  without  a  battery  !  The  disturbance  to  telegraphic  communi- 
cation was  greatest  on  lines  extending  east  and  west,  and  this  was 
largely  removed  by  using  wires  for  the  whole  circuit  instead  of  em- 
ploying the  earth  for  the  conductor  in  one  direction,  as  is  usually 
done.1 

492.  Applications  of  Electro  -  Magnetism.  —  As  electro- 
magnets are  magnetized  and  demagnetized  by  simply  clos- 
ing and  breaking  the  circuit  which  carries  the  current 
through  the  coil,  they  find  many  useful  applications.     En- 
gines have  been  made  in  which  armatures  are  attracted  in 
alternate  directions  by  different  electro-magnets  acting  at 
alternate  moments.     Such  an  armature  may  be  made  to 
carry  with  it  a  rod   to  turn  a  crank,  or,  in  some  other 
manner,  to  give  motion  to  ordinary  machinery.     For  very 
light  work  an  engine  of  this  kind  may  be  used  to  advan- 
tage, but  the  cost  of  maintaining  a  powerful  battery  is  too 
great  to  admit  of  its  economical  use  where  great  power  is 
required  and  where  steam  or  water  can  be  conveniently 
supplied. 

493.  The  Electric  Telegraph, — The  one   successful  and 
useful  application  to  which  electro-magnetism  has  been  put 
during  the  past  forty  years  is  telegraphing.     The  word 
"  telegraphing"  means  writing  at  a  great  distance,  and  a 
"telegraph"  is  any  instrument  by  which  a  person  at  one 
place  can  make  signs  which  may  be  read  at  another  place 
some  distance  away. 

494.  History   of   the   Telegraph. — Frictional  electricity  was 
known  to  the  ancients  before  the  Christian  era,  but  conduction  and 
insulation  appear  not  to  have  been  discovered  till  1729.     Very  soon 

1  Some  connection  seems  to  exist  between  these  storms  and  the  con- 
dition of  the  sun.  (See  Sharpless  and  Philips's  Astronomy,  p.  58.) 


ELECTRICITY.  295 


after  the  discovery  of  conduction,  and  the  classification  of  bodies  as 
conductors  and  insulators,  plans  were  devised  for  carrying  conducting 
wires  on  insulating  supports  and  transmitting  through  them  charges 
of  frictional  electricity,  which  should  be  sent  in  an  order  agreed  upon 
to  represent  letters  or  words.  Systems  arranged  on  this  principle 
were  never  very  satisfactory.  One  of  the  best  employed  a  separate 
wire  for  each  letter  of  the  alphabet,  each  wire  being  supplied  with  a 
delicate  electroscope.  The  person  sending  the  message  touched  the 
wires  to  the  conductor  of  an  electrical  machine  in  such  order  as  to 
spell  out  the  message  to  be  transmitted,  and  the  person  receiving  it 
watched  the  order  of  divergence  in  the  electroscopes,  and  so  read  the 
message.  This  system  was  costly  and  cumbrous,  and  it  could  be  suc- 
cessfully operated  only  through  short  distances  (20  or  30  miles),  so 
that  it  never  came  into  general  use. 

Voltaic  electricity  was  discovered  about  1792.  Oersted's  discovery 
of  the  deflection  of  the  magnetic  needle  was  made  in  1820,  and  was 
soon  applied  by  Wheatstone1  and  others  to  successful  systems  of 
telegraphing. 

495.  The  Morse  Telegraph. — The  introduction  of  the  electro- 
magnet as  an  essential  feature  of  the  telegraph  dates  back  to  about 
1836,  when  Samuel  F.  B.  Morse2  invented  the  electro-magnetic  tele- 
graph now  in  general  use  in  civilized  countries.  His  original  device 
consisted  of  a  register  (Fig.  279)  for  receiving  the  message,  and  a  key 
(see  Fig.  280)  for  transmitting  it.  The  register  is  easily  understood 
from  the  figure.  The  current  from  the  line  wire  passes  through  the 
coils  of  the  electro-magnet,  which  is  thus  rendered  magnetic,  and 
draws  down  the  armature.  This  elevates  the  point  shown  on  the 
opposite  end  of  the  lever.  The  paper  is  drawn  at  a  uniform  rate  be- 
tween the  rollers  by  the  action  of  the  weight  under  the  table.  When 
the  point  is  pressed  against  the  paper  it  describes  a  straight  line,  whose 
length  is  proportional  to  the  time  the  point  is  held  there.  This  is  de- 
termined by  the  operator  at  the  distant  station,  who  alternately  de- 
presses and  elevates  his  key.  While  he  holds  the  key  down  the 
current  passes,  the  armature  is  held  down,  and  the  point  is  pressed  up. 
Long  and  short  dashes  (called  respectively  "  dashes"  and  "  dots")  and 
vacant  spaces  are  thus  recorded  in  succession  on  the  strip  of  paper, 

1  Charles  Wheatstone,  English,  1802-1875,  professor  at  King's  Col- 
lege, London. 

2  American,  1791-1872.     The  inventor  of  the  form  of  telegraph- 
receiver  in  common  use. 


296  NATURAL   PHILOSOPHT. 

and,  as  a  definite  group  of  these  dots  and  dashes  represents  each  letter, 
figure,  and  other  mark  used,,  the  receiving  operator  is  able  to  inter- 


FIG.  279. — TELEGRAPH-REGISTER. 

pret  them.  The  accompanying  line  of  dashes  and  hyphens  represents 
the  appearance  of  such  a  message.  The  letters  above  them  are  in- 
tended as  a  translation,  for  the  benefit  *of  the  readers  of  this  book. 

"Wil      1       comeattenAM 

The  striking  of  the  lever  against  the  screws  which  regulate  the  dis- 
tance of  its  motion  makes  an  appreciable  sound,  and  a  certain  differ- 
ent combination  of  these  is  used  to  call  the  attention  of  each  particu- 
lar operator  on  a  given  line. 

Soon  after  this  system  came  into  use,  operators  discovered  that  they 
could  read  the  messages  as  well  as  the  office-call  by  the  click  of  the 
lever  against  the  screws,  and  the  paper  was  dispensed  with.  A  new 
form  of  instrument,  known  as  the  sounder,  now  takes  the  place  of  the 
register  in  most  telegraph-offices.  Its  general  structure  may  be  under- 
stood from  Fig.  280.  Th£  lever  is  drawn  down  by  the  electro-magnet, 
and  strikes  against  a  solid  metal  piece,  making  a  loud  sound.  A 
spring  is  so  attached  to  an  arm  connected  with  the  lever  that  it  in- 
stantly raises  the  lever  on  the  breaking  of  the  current. 

"When  a  telegraph  line  is  long,  the  resistance  of  the  wire  renders 
the  current  feeble,  so  that  the  sounder  is  not  operated  with  sufficient 
force  to  be  satisfactory  under  all  circumstances.  To  remedy  this,  a 
local  battery  is  introduced  at  each  station  to  operate  the  sounder  at 


ELECTRICITY. 


297 


that  station.  The  circuit  of  this  battery  (the  "local  circuit")  is 
opened  and  closed  by  a  relay,  which  in  turn  is  operated  by  the  feeble 
current  of  the  line- wire.  The  "relay"  is  a  very  delicate  electro- 
magnet, operating  a  lever  whose  end  is  made  to  strike  against  a  metal 
piece  and  thus  close  the  local  circuit. 

Pig.  280  represents,  in  vertical  section,  a  Morse  telegraph-station, 
such  as  may  be  seen  in  almost  any  town  or  at  almost  any  railroad- 
station.  The  student  will  please  trace  out  the  office  and  action  of 
each  piece  of  apparatus.  The  key,  the  sounder,  and  the  relay  may 
be  supposed  on  a  table,  and  the  local  battery  under  it.  The  wire  of 
the  main  line  is  seen  entering  at  one  side  and  leaving  at  the  other. 
The  key  must  be  kept  "  closed"  at  all  times,  except  in  the  particular 
office  on  a  line  from  which  a  message  is,  at  the  time,  being  sent.  The 
current  in  Fig.  280  we  will  suppose  enters  at  the  left,  passes  through 
the  key,  and  by  the  wire  to  the  relay,  around  the  coils  of  the  electro- 
magnet in  the  relay,  and  out  at  the  right,  going  in  the  same  way 
through  all  the  offices  which  are  in  the  main-line  circuit.  When  no 
message  is  traversing  the  line,  the  current  is  continuous,  the  cores  of 
all  the  relays  are  magnets,  and  the  armatures  are  all  held  against  the 
opposing  anvils.  This  closes  the  local  circuits  and  holds  down  the 
levers  of  the  sounders.  When  a  message  is  to  be  sent  from  any  office 
on  the  line  to  any  other  office,  the  operator  in  the  sending  office  opens 
his  key.  This  breaks  the  circuit,  stops  the  current,  and  demagnetizes 
the  relay,  whose  spring  pulls  back  the  armature.  This  in  turn  breaks 
the  local  circuit  and  demagnetizes  the  sounder,  whose  lever  is  raised 
by  its  spring.  This  is  the  condition  of  things  shown  in  the  figure. 


Zine  Wire 


local. 

FIG.  280.— DIAGRAM  OF  MORSE  TELEGRAPH  STATION. 

The  sender  then  operates  his  key  by  pressing  it  down  and  raising  it 
at  certain  intervals.  The  currents  thus  sent  operate  on  the  relay  situ- 
ated in  each  office  of  the  line,  and  its  armature  vibrates,  keeping  time 
with  the  motions  of  the  sender's  key.  This  acts  as  a  key  for  the  local 
circuit,  and  a  succession  of  currents  is  sent  through  it,  operating  the 
sounder.  Thus  it  will  be  seen  that  a  message  sent  from  any  one 


298  NATURAL   PHILOSOPHY. 


station  to  any  other  station  may  be  read  at  all  the  stations  in  the  main 
circuit.  The  sending  operator  even  reads  his  own  message. 

496.  The  Earth  Used  as  a  Conductor. — In  all   ordinary  tele- 
graph and  telephone  lines  the  earth  is  used  as  a  conductor  in  one  di- 
rection, and  but  one  wire  is  employed.     Most  lines  of  telegraph  have 
a  battery  at  each  end,  the  positive  electrode  of  one  battery  and  the 
negative  of  the  other  being  connected  with  the  same  wire.     The  other 
electrode  of  each  battery  is  connected  with  a  "  ground- wire,"  which 
is  attached  to  a  metallic  plate  buried  in  moist  earth. 

497.  Duplex  and  Quadruplex  Telegraphy. — The  simple  Morse 

system,  just  described,  is  very  reliable,  but  a  given  wire  can  transmit 
only  one  message  at  a  time.  Various  arrangements  have  recently 
been  devised  by  which  a  wire  may  be  made  to  convey  one  or  two 
messages  each  way  at  the  same  time  without  conflict.  The  former  is 
known  as  the  duplex  system,  and  the  latter  as  the  quadruplex  system. 
A  complete  explanation  of  them  would  take  us  beyond  the  limit  of 
this  work. 

The  art  of  telegraphy  is  advancing  very  rapidly.  Mechanical  ar- 
rangements for  transmitting  are  successfully  employed,  and  auto- 
matic arrangements  for  receiving  and  for  retransmitting  if  desired. 
The  simple  Morse  system  was  a  marvel  of  completeness  and  rapidity. 
A  good  operator  can  send  or  receive  30  or  40  words  per  minute, — as  fast 
as  a  rapid  penman  can  write.  This  was  the  capacity  of  a  single  wire 
until  recently.  With  a  combination  of  the  latest  inventions  the  feat 
has  been  accomplished  of  transmitting  1500  words  between  New 
York  and  Boston  over  the  same  wire  in  one  minute. 

498.  Ocean  Cables. — On  land  lines  the  line-wire,  even  if  very 
long,  is  charged  and  discharged  nearly  instantly,  and  the  current  is 
no  appreciable  length  of  time  in  traversing  it.     Ocean  cables,  being 
laid  under  water,  must  be  surrounded  by  an  insulator.     Gutta-percha 
is  used.     The  arrangement  then  resembles  a  Leyden  jar,  the  con- 
ducting wire  representing  the  inside  coat,  and  the  water  the  outside 
coat,  while  the  gutta-percha  acts  as  the  glass.     To  charge  this  re- 
quires some  time,  and  to  discharge  it  requires  as  long.     In  the  cable 
between  Ireland  and  Newfoundland  this  amounts  to  a  total  of  six 
seconds.     On  this  account  special  instruments  are  required  for  send- 
ing and  receiving  messages  over  ocean  cables. 

499.  Electric  Clocks. — The  electric  current  is  frequently  used  to 
propel  or  regulate  clocks.     The  pendulum  of  a  standard  clock  is  made 
to  operate  a  key,  which  opens  and  closes  a  circuit  including  all  the 
clocks  to  be  regulated.     These  may  be  distributed  over  a  large  build- 


ELECTRICITY.  299 


ing,  or  a  town,  or  along  a  railroad  line.  The  interrupted  current 
passes  through  an  electro-magnet  in  each  clock.  The  armature, 
moving  in  exact  unison  with  the  beats  of  the  standard  clock,  either 
operates  on  a  ratchet-wheel  and  communicates  motion  to  the  clock, 
or  regulates  the  swinging  of  a  pendulum.  In  either  case  all  the 
clocks  will  keep  exactly  together  and  with  the  regulator. 

500.  Thermal  Electricity. — If  a  bar  of  antimony  (A,  Fig. 
281)  and  a  bar  of  bismuth,  B,  be  soldered  together  at  one 
end,  and  the  junction  be  moderately  heated,  and  wires  at 
the  other  end  be  connected  with  the  coils  of  a  galvanome- 
ter, an  electric  current  is  found  to  exist  flowing  from  the 
antimony  through  the  wire  to  the  bismuth,  and  from  the 
bismuth  across  the  heated  junction  to  the  antimony.  If 
the  junction  be  cooled  instead  of  being  heated,  a  current  is 
established  in  the  opposite  direction. 

If  a  large  number  of  such  bars  be  joined  together  in 
series,  as  shown  in  Fig.  282,  a  very  slight  amount  of  heat- 


FIG.  281.— THERMO-ELECTRIC  PAIR.  FIG.  282.— PRINCIPLE  OF  THERMOPILE. 

ing  or  cooling  of  the  junctions  at  one  end  makes  an  appre- 
ciable current,  the  current  always  flowing  at  the  warmer 
junctions  from  bismuth  to  antimony,  and  at  the  cooler  from 
antimony  to  bismuth.  The  same  effect,  in  a  less  degree,  is 
produced  by  substituting  other  metals  for  the  antimony 
and  bismuth.  Two  metals  so  arranged  are  called  a  thermo- 
electric pair,  and  a  combination  of  several  (usually  twenty- 
five  to  one  hundred)  such  pairs  constitute  a  thermopile. 
When  connected  with  a  galvanometer  it  is  known  as  the 
thermo-multiplier,  one  of  the  most  delicate  of  thermometers. 
501.  Induced  Currents. — If  a  coil  of  wire,  around  which 
a  battery  current  is  flowing,  be  introduced  into  a  larger 
coil  (see  Fig.  283),  a  galvanometer  shows  that  while  the  first 
coil  is  moving  into  the  second  a  current  flows  in  the  outside 


300 


DEPARTMENT  OF 

NATURAL  PHILOSOPHY. 


coil.  On  removing  the  inside  coil,  a  current  flows  in  the 
outside  coil.  This  is  an  induced  current,  and  it  lasts  only 
while  one  coil  moves  towards  or  from  the  other.  The  coil  con- 
nected with  the  battery  is  called  the  primary  coil,  and  the 


FIG.  283.— PRIMARY  AND  SECONDARY  CURRENTS 

other  the  secondary  coil.  Every  motion  of  the  primary 
coil  towards  or  into  the  secondary  coil  produces  a  current 
in  the  secondary  coil  opposite  in  direction  to  that  in  the 
primary ;  and  every  motion  of  the  primary  from  or  out 
of  the  secondary  produces  a  current  in  the  secondary  in 
the  same  direction  as  that  in  the  primary. 

If  the  primary  coil  be  dropped  into  the  secondary  and 
allowed  to  remain,  no  induced  current  is  noticed  after  the 
primary  coil  is  inserted,  so  long  as  the  primary  current  is 
constant.  Any  increase  in  the  strength  of  the  primary  cur- 
rent induces  an  inverse  current  (i.e.,  opposite  in  direction  to 
its  own)  in  the  secondary  coil,  and  any  decrease  in  the 
strength  of  the  primary  current  induces  a  direct  current  in 
the  secondary.  If  the  primary  circuit  be  alternately  closed 
and  opened  while  the  coil  remains  in  the  secondary,  it  is 
found  that  every  time  the  circuit  is  closed  an  inverse  mo- 
mentary current  is  induced  in  the  secondary,  and  whenever 
it  is  opened  a  direct  momentary  current  is  induced.  These 


ELECTRICITY. 


301 


iast  currents  have  a  great  electro-motive  force,  will  jump  a 
considerable  distance  through  air,  and  exhibit  other  prop- 
erties of  frictional  electricity.  They  will  be  more  fully 
treated  of  in  Art.  513. 

If,  instead  of  a  primary  coil,  a  magnet  be  used,  its  ap- 
proach induces  a  current  in  one  direction,  and  its  removal 
induces  a  current  in  the  opposite  direction.  If  an  iron 
core  be  placed  in  the  secondary  (Fig.  284),  opposite  cur- 


FIG.  284. — CURRENT  INDUCED  BY  MAGNET. 


rents  are  induced  by  the  approach  and  withdrawal  of  either 
pole  of  the  magnet.  These  currents  are  stronger  than 
those  induced  by  the  same  magnet  in  the  same  coil  without 
the  iron  core.  This  is  because  the  magnet  acts  by  induc- 
tion on  the  iron  and  makes  it  a  magnet  (Art.  412).  If, 
now,  the  magnet  be  placed  in  the  coil,  and  the  piece  of  iron 
be  suddenly  moved  towards  it  and  away  from  it,  the  same 
alternating  currents  will  be  induced,  the  iron  acting  as  a 
magnet.  If  these  currents,  instead  of  being  passed  through 
a  galvanometer,  as  shown  in  Fig.  284,  be  passed  through  a 
second  coil  surrounding  a  magnet,  they  vary  the  strength 
pf  the  magnet,  the  current  in  one  direction  adding  to  its 
strength,  on  the  principle  of  the  electro-magnet,  and  that 
in  the  other  direction  taking  from  it. 

26 


302  NATURAL  PHILOSOPHY. 

502.  The  Telephone. — The  last  article  explains  the  principle 
of  the  Bell  telephone,  which,  although  first  publicly  exhibited  at  the 
time  of  the  Centennial  Exhibition  in  1876,  is  now  in  very  extensive 


FIG.  285. — SECTION  OF  BELL  TELEPHONE. 

use  throughout  the  civilized  world.  Fig.  285  shows  the  instrument 
in  section.  NS  is  a  steel  magnet.  B  is  the  coil  of  fine  wire,  whose 
ends  are  connected  by  the  binding  screws  with  the  line-wires  CC. 
LL  is  a  sheet  of  very  thin  iron,  called  the  diaphragm.  The  whole  is 
enclosed  in  a  neat  rubber  tube,  M,  and  supplied  with  a  mouth-piece 
(and  ear-piece),  RR/.  To  send  a  message,  the  operator  speaks  into  the 
mouth-piece.  The  sound  throws  the  air  into  vibration,  and  this  in 
turn  communicates  its  motion  to  the  diaphragm.  The  diaphragm, 
being  so  near  the  magnet,  is  polarized  by  induction.  As  it  is  pushed 
towards  the  magnet  by  the  sound-waves  it  induces  a  current  in  one 
direction  in  the  coil  of  wire,  and  as  it  recedes  it  induces  a  current  in 
the  opposite  direction.  These  alternating  currents,  agreeing  in  fre- 
quency with  the  sound-waves  made  by  the  operator's  voice,  are  propa- 
gated through  the  wires  to  the  distant  station,  and  are  there  received 
by  an  instrument  exactly  similar  to  the  transmitting  instrument.  Of 
these  rapidly  alternating  currents,  those  in  one  direction  strengthen 
the  steel  magnet,  and  those  in  the  other  direction  weaken  it.  It  thus 
exerts  a  varying  amount  of  attraction  on  the  diaphragm  and  causes 
it  to  vibrate,  the  vibrations  keeping  time  with  the  alternations  of  the 
current,  which  in  turn  keep  time  with  the  vibrations  of  the  trans- 
mitting diaphragm,  and  as  this  keeps  time  with  the  vibrations  of  the 
operator's  voice,  the  sound  of  his  voice  is  reproduced  at  the  distant 
station.  Fig.  286  represents  the  two  terminal  stations  of  a  telephone 
line,  connected.  The  letters  correspond  with  those  in  Fig.  285. 
There  may  be  any  number  of  telephones  on  the  line,  and  the  cir- 


ELECTRICITY.  3Q3 


cuit  may  be  completed  by  using  ground-wires,  as  with  the  telegraph. 
There  should  be  two  instruments  at  each  station,  one  for  the  operator 
to  hold  to  his  ear  and  one  to  his  mouth.  A  battery  current  is  sent 
through  to  an  alarm-bell  (Art.  505)  to  call  attention  when  a  message 
is  to  be  sent. 


Line  Wire. 


R/L 


\ 


FIG.  286.— DIAGRAM  OF  BELL  TELEPHONE  LINE. 


503.  The  telephone  is  a  beautiful  illustration  not  only  of  electro- 
magnetic induction,  proving  the  close  connection  between  electricity 
and  magnetism,  but  also  of  the  transformation  of  energy,  and  of  the 
correlation  of  the  physical  forces  (Art.  83).     The  sound-waves  set 
the  diaphragm  into  vibration  ;  the  force  of  its  motion,  by  reaction  on 
the  magnetic  pole,  appears  as  the  electric  force  in  the  wire ;  this  is 
transformed  into  magnetic  force  at  the  other  end  of  the  wire,  which 
is  made  known  to  us  by  the  vibration  of  the  second  diaphragm,  con- 
veyed to  our  ear  through  the  medium  of  the  air,  just  as  it  would 
have  been  had  our  ear  been  near  enough  to  catch  the  vibrations  in  the 
air  produced  by  the  speaker's  voice! 

504.  The  Telephone  Current  Feeble.— The  telephone  current 

is  very  feeble.  It  has  been  estimated  that  the  force  represented  by 
the  amount  of  heat  required  to  raise  one  gram  of  water  one  degree 
Centigrade  would  be  sufficient  to  impress  10,000  words  on  a  Bell 
telephone.  This  would  be  more  than  twenty  pages  of  the  large  type 
of  this  book. 

Many  wonderful  and  useful  recent  inventions  are  applications  of 
feeble  currents  thus  induced  in  what  might  be  termed  secondary  coils, 
or  of  the  slight  changes  in  strength  of  primary  currents. 

505.  The  Alarm-Bell. — The  attention  of  the  receiving  operator 
of  a  telephone  message  is  called  by  a  bell  similar  to  those  employed 
in  burglar-  and  fire-alarms,  and  in  hotels  and  other  large  buildings 
as  call-bells.     The  operation  of  such  a  bell  will  be  readily  understood 
from  Fig.  287.    The  current  passes  in  at  one  of  the  "  binding  screws," 
AD,  and  out  at  the  other,  traversing  the  coils  of  the  electro-magnet. 
The  core  is  thus  rendered  magnetic,  and  the  armature,  B,  is  drawn 
forward,  causing  the  hammer,  M,  to  strike  the  bell.      The  current 


304 


NATURAL   PHILOSOPHY. 


on  its  way  from  A  to  D  passes  up  through  the  armature,  B,  and  down 
through  the  spring,  K.  When  B  is  drawn  forward,  contact  with  the 
spring,  R,  is  broken,  and  the  current  ceases.  The  core  is  thus  de- 


FIG.  287. — ELECTRIC  BELL. 

magnetized,  and  B  is  released  and  thrown  back  by  the  small  spring 
at  the  bottom.  This  again  closes  the  circuit,  and  the  operation  is  re- 
peated, in  most  cases  several  times  in  a  second,  as  long  as  the  current 
is  sent. 


IV.— MAGNETO-ELECTRICITY  AND  DYNAMO-ELECTRIC  MACHINES. 

506.  Currents  produced  by  Magnetism. — Eeferring  again 
to  Art.  501,  we  find  that  the  approach  of  a  magnetic  pole 
to  a  coil,  and  the  withdrawal  of  it  from  the  coil,  induce 
currents  in  the  coil.  If  the  pole  be  stationary,  and  the  coil 
(better  with  an  iron  core)  be  moved,  the  same  currents  re- 
sult. This  is  Faraday's  discovery,  made  in  1831,  and  he 
showed  that  such  currents  result  in  all  conductors  which 
move  in  the  magnetic  field  (the  space  strongly  influenced 
by  the  magnet)  in  any  direction  other  than  parallel  to  the 


ELECTRICITY. 


305 


lines  of  force  (Art.  420).  A  current  so  developed  possesses 
the  properties  of  voltaic  electricity.  It  is  now  largely  em- 
ployed for  producing  the  electric  light,  and  for  driving 
electric  motors.  A  description  of  the  apparatus  used  for 
generating  it  will,  therefore,  be  in  place  here. 

507.   Clarke's  Machine, — One  of  the  original  forms  of  magneto- 
electric  machine  is  shown  in  Fig.  288.     Its  operation  is  plainly  indi- 


FIG.  288.— CLARKE'S  MAGNETO-ELECTRIC  MACHINE. 

cated.  The  two  coils  of  wire  with  soft  iron  cores  are  made  to  rotate 
rapidly  about  the  horizontal  axis,  so  that  each  one  is  brought  oppo- 
site each  of  the  magnet's  poles  in  each  revolution.  As  each  coil  ap- 
proaches each  pole,  a  current  is  generated  in  it  in  one  direction,  and 
as  it  recedes,  a  current  is  generated  in  the  opposite  direction.  These 
currents  are  conveyed  to  the  wires,  and,  on  account  of  their  intermit- 
tent nature,  they  produce  a  peculiar  shaking  or  "  shocking"  sensation 
on  passing  through  the  body.  The  machine  here  shown  is  intended 
u  26* 


306  NATURAL   PHILOSOPHY. 

for  giving  such  shocks.  The  currents  may  either  be  allowed  to  flow 
through  the  wires  in  alternate  directions,  or,  by  means  of  a  mechani- 
cal device  known  as  a  commutator,  all  the  positive  currents  may  be 
delivered  to  one  of  the  wires,  and  all  the  negative  to  the  other,  thus 
making  the  currents  all  "  flow  in  the  same  direction." 

508.  History  of  Magneto-Electricity.  —  By  employing  a 
large  number  of  powerful  horseshoe  magnets  and  a  larger 
number  of  revolving  coils,   machines  on  this  plan  were 
made,  under  the  supervision  of  Faraday  and  others,  which 
gave  currents  of  sufficient  intensity  to  be  used  in  electro- 
plating, electric  lighting,   etc.     In  1866  it  was  discovered 
by  Wilde  that  the  current  from  a  large  magneto-electric 
machine,  conveyed  around  the  coil  of  an  electro-magnet, 
endued  it  with  a  magnetic  strength  far  greater  than  that 
of  the  whole  series  of  steel  magnets  used  to  generate  the 
current.     A  fresh  and  larger  armature1  was  made  to  re- 
volve before  the  poles  of  the  electro-magnet  thus  formed, 
and  from  this  armature  a  very  powerful  current  was  ob- 
tained.    This  in  turn  was  made  to  magnetize  a  second 
electro-magnet,  and  from  an  armature  revolving  in  front 
of  its  poles  a  current  was  obtained  far  exceeding  anything 
previously  known. 

509.  Dynamo-Electric  Machines. — The  next  step  in  the 
manufacture  of  magneto-electric  machines,  or,  as  they  are 
now  commonly  called,  dynamo- electric  machines,  consisted 
in  raising  the  power  of  an  electro-magnet  by  its  own  induced 
currents.     When  the  iron  core  of  an   electro-magnet  has 
been  once  magnetized,  it  retains  for  a  long  time  a  slight 
amount  of  residual  magnetism.     An  armature  revolving 
before  the  poles  of  such  an  electro-magnet  has  very  feeble 
currents  developed  in  it.     These  are  carried  through  the 
coil  of  the  electro-magnet,  increasing  its  strength.     This 
increases   the   current    in    the    armature,    which   further 
strengthens  the  power  of  the  electro-magnet,  and  so  the 

1  The  "  armature"  in  magneto-electric  machines  is  the  whole  series 
of  the  revolving  coils  with  soft  iron  cores. 


ELECTRICITY.  3Q7 


current  and  the  magnet  strengthen  each  other,  the  limit 
being  fixed  by  the  power  of  the  machine  which  gives  ro- 
tation to  the  armature.  The  armature  with  the  current 
flowing  in  it,  and  the  magnetic  pole  which  produce's  the 
current,  repel  each  other  as  similar  magnetic  poles  do; 
hence  the  necessity  of  force  to  overcome  this  repulsion. 
Of  course,  the  stronger  the  magnet  and  the  stronger  the 
current,  the  more  force  will  be  required ;  and,  as  there  is 
no  limit  to  either,  the  power  of  the  driving-engine  decides 
the  strength  of  the  current.  The  current  which  thus  ex- 
cites the  electro-magnet  passes,  after  leaving  it,  over  con- 
ducting wires  wherever  wanted,  and  becomes  the  current 
of  the  machine.  If  this  current  is  made  to  flow  through 
the  armature  of  another  similar  machine,  it  rotates  the  ar- 
mature backward,  by  virtue  of  the  repulsion  above  alluded 
to,  and  the  force  with  which  it  rotates  is  equal  to  that  ap- 
plied to  the  first  machine,  except  that  which  appears  as 
heat,  caused  by  the  resistance  of  the  conducting  wire,  fric- 
tion of  parts,  etc. 


DYNAMO-ELECTRIC  MACHINE. 


Fig.  289  represents  the  Brush  dynamo-electric  machine,  one  of  the 
many  patterns  constructed  on  plans  essentially  as  described.  It  is 
selected  for  illustration  here  on  account  of  its  very  extensive  use  in 
this  and  other  countries  for  electric  illumination. 

The  armature,  which  is  represented   between  the  large  electro- 


308 


NATURAL   PHILOSOPHY. 


magnets,  M,  is  rotated  by  the  pulley-wheel,  P.  The  currents  gener- 
ated in  the  coils,  or  "  bobbins,"  C,  of  the  armature  are  made  to  flow 
in  the  same  direction  by  means  of  a  commutator.  They  are  then  col- 
lected by  the  contact-springs,  S,  and  conveyed  through  the  wires  sur- 
rounding the  electro-magnets,  M,  and  extending  wherever  the  current 
is  wanted. 

510.  The  Electric  Arc. — As  previously  stated,  current  elec- 
tricity does  not  jump  a  break  of  any  appreciable  width  in  the 
conducting  wire.  Whenever  a  circuit  is  broken,  however,  a 
momentary  spark  is  noticed  at  the  break, 
unless  the  current  be  quite  feeble.  This 
spark  is  due  to  a  few  of  the  particles  of 
the  conducting  wire  being  carried  over 
in  an  attempt  to  keep  up  the  current. 
They  are  rendered  incandescent  because 
of  the  increased  resistance  (Art.  473)  of 
their  small  number.  If  two  pieces  of 
gas  carbon,  placed  end  to  end,  be  intro- 
c  duced  into  the  circuit  of  a  powerful  bat- 
tery, or  of  a  dynamo  machine,  and  then 
gradually  separated  to  the  distance  of 
about  a  half-inch,  particles  of  incan- 
descent carbon  travel  across  the  break, 
producing  the  most  brilliant  of  artificial 
lights.  The  light-giving  area  has  the 
form  of  a  crescent,  and  on  this  account 
is  called  the  electric  arc.  A  light  so  pro- 
duced is  called  an  arc  light,  to  distin- 
guish it  from  the  incandescent  lights,  of 
which  the  Edison  lamp,  previously  ex- 
plained, is  a  type. 

511.    The    Brush    Electric    Lamp—. 

There  are  many  forms  of  lamp  for  producing 
the  arc  light.  Fig.  290  represents  the  Brush  lamp.  The  light  is 
produced  in  the  space  between  the  two  carbons,  kk.  One  of  the  con- 
ducting wires  is  connected  with  the  lower  carbon  by  the  binding 
screw  shown,  and  the  other  wire  is  so  connected  that  the  current 


FIG.  290.— BRUSH'S  ELEC- 
TRIC LAMP. 


ELECTRICITY.  3Q9 


passes  through  the  coil,  a,  and  then  to  the  sliding-rod,/,  which  holds 
the  carbon  at  its  lower  extremity.  When  the  current  is  turned  into 
the  lamp,  the  points,  kk,  are  together.  The  current  passing  mag- 
netizes the  iron  core,  d,  of  the  coil,  a,  and  draws  it  into  the  coil,  thus 
separating  the  carbons  and  producing  the  light.  As  the  carbons  are 
drawn  farther  apart,  the  resistance  increases,  the  current  becomes 
more  feeble,  the  coil,  a,  becomes  weaker,  and  stops  raising  the  core,  d. 
The  strength  of  the  current  and  the  distance  of  the  carbons  thus  main- 
tain a  constant  balance.  When  the  current  is  shut  off  from  the  lamp 
the  carbons  fall  together  again.  The  carbons  are  gradually  con- 
sumed. The  mechanism  below  the  coil,  not  well  shown  in  the  figure, 
is  for  lowering  the  sliding-rod,/,  through  the  iron  core,  d,  so  that 
the  carbons  may  be  kept  at  a  uniform  distance  from  each  other,  no 
matter  how  long  or  how  short  they  may  be. 

512.  Methods  of  Electric  Illumination, — Of  course  any  judi- 
cious combination  of  current-producing  machinery  aifd  lamp  will 
produce  the  electric  light.     For  street  illumination,  railroad  depots, 
etc.,  the  dynamo  machine  and  the  arc  lamp  seem  well  adapted.     For 
houses,  the  incandescent  light  is  by  far  the  more  satisfactory,  not 
having  the  flicker  of  the  arc  light.     In  large  communities- a  dynamo 
machine  will  furnish  a  current  economically.     For  isolated  families, 
the  hope  for  a  satisfactory  electric  light  seems  to  rest  on  the  perfecting 
of  the  secondary  battery  (Art.  481). 

513.  The  Ruhmkorff  Induction-Coil—  As  stated  in  Art. 
501,  currents  of  great  electro-motive  force  are  generated 
in  a  secondary  coil  at  the  instants  of  starting  and  stopping 
the  current  in  the  primary  coil.     These  currents  not  only 
possess  the  characteristics  of  frictional  electricity,  but  the 
discharges  may  be  obtained  from  such   an  induction-coil 
with  much  more  uniformity  than  from  an  electrical  ma- 
chine, and  the  coil  is  not  perceptibly  affected  by  atmos* 
pheric  conditions.     Such  being  the  case,  a  description  of 
the  Euhmkorff l  coil,  and  of  some  of  the  effects  which  may 
be  produced  by  it,  is  here  inserted. 

Fig.  291  gives  a  general  view  of  the  coil,  mounted.  The  current 
from  the  battery  enters  by  the  binding-posts,  AA7.  C  is  the  com- 
mutator for  reversing  the  current  so  that  it  may  be  made  to  flow 

1  German,  settled  in  Paris;  has  gained  distinction  from  this  form 
of  induction-coil. 


310 


NATURAL  PHILOSOPHY. 


either  way  through  the  primary  coil  at  pleasure.     At  r  is  seen  the 
iron  core  of  the  primary,  and  a  small  section  of  the  primary  coil 


FIG.  291. — KUHMKORFF'S  INDUCTION-COIL. 

may  be  seen.  The  secondary  coil  is  much  larger  than  the  primary, 
and  forms  the  large  cylinder.  The  ends  of  the  wire  forming  the 
secondary  are  seen  at  BB'.  The  primary  circuit  is  automatically 
closed  and  opened  hy  the  "  break,"  n.  The  current  traverses  the  post 
at  the  left  of  n,  then  by  way  of  the  spring  and  screw  to  the  right- 
hand  post,  then  by  way  of  the  wire,  etc.  In  the  figure  the  circuit  is 
closed.  The  iron  core,  extending  entirely  through  the  coil,  is  thus 
magnetized,  and  attracts  the  disk  on  the  spring,  n,  drawing  it  away 
from  the  end  of  the  screw  and  breaking  the  current.  As  soon  as  the 
current  is  broken,  the  spring  flies  back  against  the  screw,  thus  starting 
the  current  again.  The  core  again  attracts  the  disk,  and  so  the  cur- 
rent is  made  and  broken  several  times  in  a  second. 

As  previously  stated,  the  breaking  of  the  primary  current  induces 
a  direct  current  in  the  secondary,  and  the  making  of  the  primary 
current  an  inverse  current  in  the  secondary.  This  may  be  remem- 
bered by  supposing  the  direct  current  in  the  secondary  to  be  a  mo- 
mentary continuation  of  the  force  of  the  primary  current  after  it  is 
broken,  and  the  inverse  current  to  be  a  reaction  on  the  secondary 
wire  by  the  starting  of  the  primary  current,  just  as  a  horse  in  starting 
a  heavy  load  tends  to  slip  backward.  The  direct  current  has  very 


ELECTRICITY.  31 1 


much  more  electro-motive  force  than  the  inverse  current  has ;  in  fact, 
with  ordinary  coils  the  effect  of  the  inverse  current  is  not  noticed ; 
it  is  the  direct  current,  or  that  produced  when  the  primary  current  is 
stopped,  that  produces  the  results  which  we  witness.  The  positive 
electrode  of  the  secondary  coil  is  that  from  which  the  direct  current 
flows,  and  the  negative  electrode  is  that  towards  which  the  direct  cur- 
rent flows.  To  give  the  direct  current  its  maximum  effect,  the  break 
of  the  primary  circuit  must  be  made  instantaneously.  Though  we 
adopt  a  mechanical  device  which  accomplishes  this  result,  it  is  found 
that  an  "  extra  current"  :  lingers  for  a  sensible  length  of  time  in  the 
primary  coil  and  interferes  with  the  intensity  of  the  secondary  cur- 
rent. To  correct  this  a  condenser  (Art.  453)  is  connected  with  the 
primary  circuit.  This  consists  of  several  sheets  of  tin-foil,  separated 
by  varnished  paper,  placed  in  a  drawer  in  the  base  of  the  coil.  In 
the  figure  the  connections  with  the  condenser  are  shown  at  pp.  The 
sheets  are  connected  alternately  with  the  parts  of  the  conducting  wire 
towards  the  respective  poles  of  the  battery.  "When  the  current  is 
broken,  the  extra  current  spends  itself  in  charging  this  condenser, 
which  immediately  discharges  itself  through  the  wire  in  the  opposite 
direction,  and  thus  assists  in  exciting  the  secondary  current. 

The  effectiveness  of  the  Kuhmkorff  coil  increases  with  the  length 
of  the  wire  in  the  secondary  coil.  As  those  layers  of  wire  which  are 
nearest  to  the  primary  are  most  powerfully  affected,  it  is  desirable  to 
have  all  as  near  as  possible.  For  this  reason  the  secondary  is  of  very 
fine  wire,  not  more  than  T£7  of  an  inch  in  diameter.  The  best  coils 
contain  several  miles  of  such  wire,  from  20  to  50  being  a  not  uncom- 
mon quantity.  The  great  coil  of  William  Spottiswoode  contains  280 
miles  in  the  secondary  coil.  It  forms  a  cylinder  37£  inches  long  and 
20  inches  in  diameter,  and  will  give  a  spark  42£  inches  long.  An 
induction-coil  about  6  by  2  inches,  and  giving  a  half-inch  spark,  is  a 
very  convenient  apparatus  for  administering  electric  shocks. 

514.  The  Ruhmkorff  Discharge. — The  discharge  of  the 
Ruhmkorff  coil  may  be  used  in  many  experiments  of  the 
kind  indicated  for  frictional  and  Holtz  machines  and  the 
Leyden  jar,  but  it  gives  the  most  interesting  results  when 
made  to  pass  through  glass  tubes  which  have  been  exhausted 

1  This  extra  current  is  induced  in  the  successive  circles  of  the  pri- 
mary coil  by  the  breaking  of  the  current  in  the  contiguous  parts. 
When  the  primary  circuit  is  a  straight  wire,  the  extra  current  is  not 
noticed. 


312 


NATURAL  PHILOSOPHY. 


of  most  of  their  gaseous  contents.  In  Art.  465  it  was 
stated  that  the  electrical  discharge,  though  taking  place 
with  difficulty  through  ordinary  air,  takes  place  quite 

readily  through  highly-rare- 
fied air.  The  same  is  true  for 
other  gases.  If  a  glass  tube 
be  filled  with  air,  hydrogen, 
oxygen,  nitrogen,  carbonic 
acid,  or  any  other  gas,  and 
then  by  means  of  an  air-pump 
most  of  the  gas  be  taken  out, 
the  passage  of  the  Kuhm- 
korff  discharge  through  the 
remaining  rarefied  gas  fills 
the  tube  with  a  glow  of  light. 
This  light  is  differently  col- 
ored for  different  gases.  The 
color  in  each  case  is  that  which 
is  due  to  the  incandescence  of 
that  particular  gas  (Art.  458). 
The  contents  of  such  a  tube 
may  thus  be  accurately  de- 
termined by  discharging  an 
induction-coil  through  it  and 
examining  the  discharge  with 
a  spectroscope  (Art.  302). 
515.  Geissler  Tubes,— Many 

beautiful  designs  of  such  exhausted 
tubes,  Geissler  tubes,  are  in  the 
market,  and  they  may  generally  he 
made  to  operate  with  quite  small 
Ruhmkorff  coils.  Fig.  292  gives 
an  imperfect  idea  of  the  discharge 
through  a  Geissler  tuhe  in  a  dark 
room.  The  tuhe  is  supported  by  being  stood  upright  in  a  glass  vase. 
At  the  two  extremities  are  platinum  wires,  sealed  into  the  glass  and 
connected  with  the  wires  leading  from  the  Ruhmkorff  coil.  The 


FIG.  292.— GEISSLER  TUBE. 


ELECTRICITY.  313 


glass  vase  and  bulbs  inside  the  tube  are  colored  with  oxide  of 
nium,  which  possesses  in  a  remarkable  degree  the  power  of  fluo- 
rescence when  illuminated  by  the  electric  spark.  The  vase  at  the 
bottom  is  filled  with  a  solution  of  sulphate  of  quinine,  which  ex- 
hibits a  similar  property.  The  uranium  fluorescence  should  be  a  light 
green,  the  quinine  a  soft  blue.  The  violet  light  in  the  rest  of  the 
tube  is  due  to  nitrogen  or  air. 

Exercises. — 1.  Suppose  the  thread  on  a  common  wood-screw  to 
represent  a  helix  and  the  middle  an  iron  core.  With  the  current 
running  from  the  point  towards  the  head,  which  pole  of  the  result- 
ing magnet  would  the  point  of  the  screw  represent  ? 

2.  How  many  ohms  of  resistance  in  a  telegraph-sounder  containing 
888  feet  of  copper  wire  fa  of  an   inch  thick?     Ans.  12. 

3.  It  is  desired  to  divide  an   electric  current  passing  between  two 
points  into  two  equal  parts  which  shall  pass  over  two  iron  wires,  a  and 
b.     The  wire  a  is  100  feet  long  and  fa  of  an  inch  in  diameter.     The 
wire  b  is  2500  feet  long  :  what  must  be  its  diameter  ?     Ans    %  inch. 

4.  When  telephone-wires  are  carried  on  the  same  poles  with  tele- 
graph-wires, and  parallel  with  them,  the  clicks  of  the  telegraph-appa- 
ratus are  distinctly  audible  in  the  telephones  :   explain  this. 

5.  A  small   island  on  the  coast  of  France   contains    the  terminal 
stations  of  two  ocean  telegraph  cables.    The  stations  are  not  connected 
by  wire,  but  frequently  the  messages  being  received    or  sent  by  one 
station  may  be  read  at  the  other  :  explain  this. 


V.-EADIANT  MATTER. 

516.  Striae  in  Vacuum-Tubes.— In  the  figure  of  the  Geiss- 
ler  tube  it  will  be  noticed  that  the  globular  section  of  violet 
light  near  the  lowermost  (negative)  platinum,  and  also  the 
light  in  the  narrow  part  of  the  tube  encircled  by  the  vase, 
exhibit  distinct  stratifications,  or  striae,  across  the  direction 
of  the  current.  These  striae,  or  alternate  light  and  dark 
bands,  seem  to  be  occasioned  by  the  motion  of  the  mole- 
cules and  their  impact  against  one  another  as  they  transmit 
the  electric  discharge  from  one  to  another  throughout  the 
length  of  the  tube.  If  this  view  is  correct,  the  bright 
bands  are  to  be  considered  as  caused  by  the  incandescence 
of  the  molecules,  due  to  their  impact  against  one  another, 
and  the  dark  bands  as  sections  in  which  the  residual  mole- 
cules are  moving,  in  the  main,  parallel  to  one  another,  with- 
out impact.  In  other  words,  a  number  of  molecules  occu- 
o  27 


314  NATURAL   PHILOSOPHY. 

pying  a  section  across  the  tube  (more  definite  if  the  tube 
be  of  small  diameter)  carry  the  discharge  a  certain  part 
of  the  length  of  the  tube  and  there  make  exchange  with 
the  next  set,  and  return  to  their  former  position,  repeating 
the  operation  with  very  great  rapidity,  acting  as  electrified 
bodies.  The  fact  that  the  stratifications  exist,  though  very 
fine,  in  comparatively  dense  gases,  and  increase  in  width 
as  the  exhaustion  of  the  tube  becomes  more  complete, 
seems  to  favor  this  view. 

517.  Discoveries    of   Dr,    Crookes.— In    1879,    William 
Crookes,  F.R.S.,  delivered  a  lecture  before  the  British  As- 
sociation, in  which  he  announced  a  new  set  of  phenomena, 
obtained  in  tubes  exhausted  far  beyond  the  point  at  which 
the  striae  and  luminous  effects  are  best  shown.     With  this 
degree  of  exhaustion,  stratification  and  all  other  evidence 
of  the  molecules  striking  against  one  another  cease,  and 
the  remaining  molecules  are  simply  repelled  with  great 
violence  from  the  end  of  the  tube  which  is  connected  with 
the  negative  pole,  and  move  in  straight  lines  until  stopped 
by  the  glass  of  the  containing  vessel  or  some  other  solid 
placed  in  their  path.     Now,  as  the  defined  characteristic  of 
gases  is  an  interaction  among  the  molecules  by  which  they 
are  constantly  repelling  one  another,  and  as  in  these  ex- 
hausted spaces  the  remaining  molecules  seem  to  move  in- 
dependently of  one  another,  and  thus  violate  the  funda- 
mental law  of  the  gaseous  condition  of  matter,  Professor 
Crookes  has  proposed  for  the  highly-rarefied  residue  ob- 
tained in  his  tubes  the  name  radiant   matter.      In  gen- 
eral, the  exhaustion  of  the  radiant-matter  tubes  may  be 
said  to  be  y.-Q--^, jpr -$  of  an  atmosphere,  or  till  they  con- 
tain but  that  fraction  of  the  air  or  other  gas  which  they 
originally  contained.     Brilliant  Geissler-tube    phenomena 
are  shown  with   tubes  containing   nearly  3000  times  as 
much  gas,  or  about  3^  of  an  atmosphere. 

518.  Radiant  Matter  repelled  from  a  Negative  Electrode.— 

The  properties  of  radiant  matter  are  best  studied  by  means  of  the 


ELECTRICITY.  315 


discharge  of  an  induction-coil.  The  molecules  are  repelled  from  the 
negative  pole,  indicating  that  in  their  natural  condition  they  are  in  a 
negatively  electrified  state.1  When  the  negative  pole  is  made  in  the 
shape  of  a  plate  with  considerable  surface,  they  are  repelled  from  the 
surface  at  right  angles  to  it,  otherwise  they  take  the  general  direction 
indicated  by  the  entrance  of  the  negative  wire. 

519.  Phosphorescence  produced  by  Radiant  Matter.— The 

particles  of  radiant  matter  produce  a  bright  phosphorescence  where 
they  strike.  Fig.  293  shows  the  form  of  a  tube  with  which  this  is 


FIQ.  293.— SHELL  TUBE. 

beautifully  illustrated.  Before  being  exhausted,  the  tube  has  had  a 
collection  of  rubies,  shells,  etc.,  placed  in  it.  On  passing  the  dis- 
charge by  means  of  the  wires  shown,  the  mineral  collection  exhibits 
in  the  dark  a  rich  glow  of  mixed  colors  and  no  inconsiderable  amount 
of  light. 

520.  Radiant  and  Gaseous  Matter  compared.— In  Fig.  294 

are  two  bulbs  which  show  in  a  striking  manner  the  difference  be- 
tween radiant  and  gaseous  matter.  The  bulb  B  contains  radiant 
matter.  The  bulb  A  is  an  ordinary  vacuum-tube  containing  about 
3000  times  as  many  molecules  of  the  original  air  as  B  does.  In 
other  respects  they  are  entirely  similar.  Each  has  a  concave  alumi- 
num plate,  a  and  a',  fastened  to  the  sealed-in  platinum  wire  for  the 
negative  electrode.  Each  has  three  other  sealed-in  platinum  wires, 
b,  c,  d,  either  of  which  may  be  made  the  positive  electrode.  The 
negative  pole  of  the  Ruhmkorff  being  connected  with  a  in  the  tube 

1  It  might  be  remarked  that  the  only  substances  which  can  be  re- 
duced to  the  condition  of  radiant  matter  are  those  elements  which  have 
long  been  known  as  the  non-metallic  or  electro-negative  elements. 


316 


NATURAL   PHILOSOPHY. 


A,  the  line  of  light  indicating  the  path  of  the  current  extends  in  a 
tolerably  direct  course  to  that  platinum  wire  which,  for  the  time 
being,  is  made  the  positive  pole,  whether  that  be  at  the  opposite  side, 


FIG.  294.— GEISSLER  TUBE  AND  RADIANT  MATTER  TUBE. 


the  top,  or  the  bottom  of  the  bulb.  When,  however,  the  plate- af  in 
the  bulb  B  is  made  the  negative  pole,  the  particles  are  driven  across 
the  tube,  as  indicated  in  the  figure,  whether  the  positive  pole  be  at  6, 
c,  or  d,  or  whether  it  be  detached  entirely.  The  point  between  c  and 
6,  where  the  molecules  strike  the  glass,  is  indicated  by  a  bright  phos- 
phorescent patch.  With  a  strong  coil  this  spot  soon  becomes  white- 
hot,  and  the  glass  actually  melts.  No  such  result  is  obtainable  with 
ordinary  vacuum-tubes. 

521.  The  "Shadow  Tube." — The  glass  of  which  most  of  these 
tubes  is  composed  is  soft  German  glass,  which  yields  a  bright  apple- 


ELECTRICITY. 


317 


green  phosphorescence  on  being  bombarded  by  the  particles  of  radi- 
ant matter.     Fig.  295  represents  a  device  for  showing  that  the  phos- 


FIG.  295.— THE  SHADOW  TUBE. 


phorescence  is  due  to  this  impact  of  the  molecules.  The  negative 
pole  a  is  a  flat  disk,  which  throws  the  molecules  towards  the  larger  end 
of  the  tube.  A  piece  of  metallic  aluminum,  6,  in  the  form  of  a  cross, 
is  so  placed  that  it  intercepts  some  of  the  molecules,  and  the  part  of 
the  glass  thus  protected  gives  no  phosphorescence,  and  remains  dark, 
resembling  a  shadow. 

522.  The  "Railway  Tube."— This  impact  of  particles  flying 
from  the  negative  pole  is  capable  of  setting  light  machinery  in  mo- 
tion. Fig.  296  represents  a  light  wheel  with  broad  mica  paddles,  set 


FIQ.  296. — THE  RAILWAY  TUBE. 

on  a  smooth  railway  in  a  highly-exhausted  tube.  When  the  disks  at 
the  ends  are  made  the  poles  of  an  induction-coil,  the  wheel  rotates 
rapidly,  and  travels  from  the  negative  towards  the  positive  pole.  By 
reversing  the  current  with  the  commutator  of  the  Kuhmkorff,  the 

27* 


318  NATURAL   PHILOSOPHY. 


wheel  is  driven  alternately  from  end  to  end  of  the  track  as  often  as 
desired. 

523.  Streams  of  Radiant  Matter  self-repellent,— Fig.  297  rep- 
resents a  piece  of  apparatus  for  demonstrating  that  a  stream  of  radi- 
ant matter  acts  as  a  line  of  electrified  bodies  moving  in  the  same 
direction,  and  not  as  a  carrier  of  an  electric  current.  The  disks  a 
and  b,  slightly  inclined  to  the  vertical,  may  either  be  made  the  nega- 
tive pole.  The  positive  pole  is  at  c.  The  back  of  the  tube  contains 
a  screen  of  phosphorescent  substance,  which  shows  the  entire  path  of 
the  particles  which  are  driven  through  the  slits  d  and  e  of  a  copper 
plate.  When  b  is  made  the  negative  pole,  the  stream  extends  from  e 
to/.  When  a  is  made  the  negative  pole,  the  stream  extends  from  d 
to/.  If  a  and  b  are  both  made  negative  poles  at  the  same  time,  by 
using  two  equal  wires  from  the  negative  pole  of  the  induction-coil, 
two  streams  of  radiant  matter  traverse  the  tube,  but  they  do  not 
converge  towarcte/,  but  move  in  parallel  or  divergent  lines  to  g  and 


FJG.  297. — Two  STREAMS  OF  BADIANT  MATTER. 

h.  This  shows  them  to  be  repellent,  and  indicates  that  they  are 
moving  charged  bodies  rather  than  conductors.  Parallel  conducting 
wires  attract  each  other. 

524.  Many  other  instructive  and  beautiful  experiments 
may  be  performed  with  these  highly-exhausted  vessels. 
Enough  are  here  given  to  indicate  that  the  very  rare  state 
of  matter  under  examination  exhibits  properties  very  dif- 
ferent from  those  of  gaseous  matter,  and  that  time  and 
further  experiments  may  fully  confirm  the  conclusion  that 
matter  exists  in  four  states,  as  mentioned  in  Chapter  I., — 
viz.,  solid,  liquid,  gaseous,  and  radiant. 


METEOROLOGY.  319 


CHAPTER  X. 
METEOROLOGY. 

525.  Meteorology  treats  of  the  atmosphere  and  the  phe- 
nomena there  noticeable.1 

526.  Climate. — Climate  means  the  conditions  of  the  at- 
mosphere, particularly  its  states  of  heat  and  moisture  that 
exist  at  any  place. 

527.  Causes  of  Climate. — The   causes   which   affect  the 
climate  are  principally  (1)  the  distance  from  the  equator, 
(2)  the  height  above  the  sea,  (3)  the  distance  from  the  sea, 
and  (4)  the  prevailing  winds. 

528.  Latitude  of  Place. — It  is  familiar  to  all  that  the 
nearer  a  country  is  to  the  equator,  as  a  rule,  the  hotter  it 
is.    The  reason  2  of  this  is  that  the  sun  shines  directly  down 
on  the  torrid  zone,  while  away  from  it  it  shines  obliquely 
and  its  rays  are  spread  over  a  great  area. 

529.  Height  above  the  Sea. — As  we  rise  above  the  sea- 
level,  it  usually  becomes  colder.     Those  who  have  gone  up 
in  balloons  speak  of  the  intense  cold  in  the  upper  regions 
of  the  air.     The  cause  of  this  is  that  in  the  rare  air  the 
body  gives  off  more  heat  than  it  receives.     Near  the  sea- 
level  the  dense  and  moist  air  serves  as  a  blanket  to  keep  in 
the  heat  which  the  earth  receives  from  the  sun.    When  the 
sun  is  shining  directly  on  a  mountain  it  may  seem  quite 

1  The  word  is  derived  from  Greek  words  signifying  "  the  science 
of  things  above  the  earth."    It  has  no  special  reference  to  meteors  or 
shooting-stars. 

2  For  a  fuller  explanation,  see  Sharpless  and  Philips's  Astronomy, 
p.  92. 


320  NATURAL   PHILOSOPHY. 


warm,  for  then  heat  is  being  taken  in  j  but  as  soon  as  a 
cloud  passes  over,  or  the  sun  sets,  the  radiation  of  heat 
begins,  and  great  cold  results.  An  Alpine  traveller  has 
said  that  the  mercury  in  a  black  bulb  thermometer  indi- 
cated 132°  while  in  the  shade  it  was  only  22°. 

Why  have  a  black  bulb  thermometer  ? 

There  is  a  temporary  exception  to  this  rule  under  certain 
conditions.  On  a  cold,  still  morning  the  thermometer  will 
indicate  a  lower  level  in  the  valleys  than  on  the  surround- 
ing hills.  This  is  because  the  cold  air,  being  heavier,  sinks 
to  the  lowest  level. 

530.  Proximity  to  the   Ocean, — The  temperature  of  a 
country  near  the  sea  varies  much  less  in  a  year  than  that 
of  one  farther  inland. 

The  cause  of  this  is  largely  the  same  as  that  explained 
in  the  preceding  paragraph.  When  the  sun's  heat-rays 
fall  on  land  they  do  not  penetrate  to  any  great  depth. 
When  the  sun  sets,  or  gets  low  down  in  winter,  the  slight 
amount  of  heat  stored  up  on  the  surface  of  the  soil  is 
quickly  lost  by  radiation,  and  cold  weather  sets  in. 

The  heat-rays  penetrate  much  more  deeply  into  the 
water.  In  clear  water  it  is  believed  that  they  affect  its 
temperature  to  a  depth  of  nearly  600  feet.  Water  has  also 
great  capacity  for  retaining  heat.  Hence  it  stores  up  large 
quantities  during  daytime  and  in  the  summer  season,  and 
parts  with  it  slowly  at  night  and  during  the  winter.  It 
therefore  tends  to  preserve  a  more  uniform  temperature 
throughout  the  year,  and  this  affects  the  climate  of  the 
lands  bordering  on  it. 

531.  Character  of  Ground. — A  sandy  or  stony  country,  as 
a  desert,  becomes  quickly  heated  when  exposed  to  direct 
rays,  and  as  quickly  cools  off  after  they   are  removed, 
while  a  country  covered  with  vegetation  retains  its  heat 
much  longer.     Evaporation  from  the  surface  of  the  leaves 
also  uses  up  some  heat,  so  that  a  fertile  and  productive 


METEOROLOGY.  321 


country  has  a  more  equable  temperature  than  a  sterile 
one. 

532.  Direction  of  Winds, — The  direction  of  the  prevail- 
ing winds  also  influences  very  considerably  the  character 
of  the  climate.     The  causes  which  affect  the  direction  of 
the  winds  will  be  explained  farther  on.    Since  winds  bring 
the  atmosphere  of  the  places  which  they  have  traversed, 
if  the  prevailing  direction  in  the  Northern  hemisphere  is 
from  the  south,  the  weather  will  be  warm,  and  if  from  the 
north,  cold,  as  compared  with  that  of  other  countries  of 
the  same  latitude.     If  the  wind  blows  in  from  the  sea,  the 
air  will  be  moist,  and  if  from  off  the  land,  dry. 

As  the  ocean  is  more  uniform  in  temperature  than  the 
land,  winds  from  off  it  will  be  of  nearly  the  same  character 
the  year  through,  while  a  country,  even  if  near  the  sea, 
which  is  frequently  subjected  to  winds  from  the  interior 
will  vary  greatly  in  climate  in  the  different  seasons. 

533.  Local  Causes. — There  are  other  causes  of  climate 
more  local  in  their  character.     If  a  place  has  a  south 
frontage,  so  that  it  is  exposed  to  the  more  direct  rays  of 
the  sun,  and  is  shielded  from  the  cold  north  winds,  its  aver- 
age temperature  will  be  higher,  and  vice  versa. 

Two  Arctic  localities  often  differ  widely  in  temperature, 
from  the  fact  that  ice  freezes  in  one  and  floats  away  and 
thaws  in  the  other.  Now,  freezing  always  liberates  heat 
from  the  water,  while  thawing,  requiring  heat,  abstracts  it 
from  the  air.  The  former  locality  will  then  be  warmer 
than  the  latter. 

The  exposure  to  the  effects  of  ocean  currents  also  pro- 
duces a  great  effect  on  the  climate.  Water,  as  we  have  seen, 
has  great  power  to  store  up  heat.  If  a  current  of  warm 
water  flows  against  the  shore,  the  heat  is  largely  given  out, 
and  the  temperature  of  the  land  is  raised.  The  Gulf  Stream 
leaves  Florida  with  a  temperature  of  about  80°.  When  it 
completes  its  circulation  and  again  reaches  the  torrid  zone, 
its  temperature  is  40°.  These  forty  degrees  of  heat  have 


322  NATURAL   PHILOSOPHY. 

been  given  to  the  land,  chiefly  Western  Europe,  thus  rais- 
ing its  temperature  considerably  above  that  of  countries  of 
the  same  latitude  in  America. 

534.  Interference  of  Causes. — It  will  thus  be  seen  that  a 
great  many  causes  go  to  produce  the  climate  of  any  place. 
It  is  often  impossible  to  tell  how  many  of  them  are  in 
operation.     Sometimes  they  work  against  one  another  to 
produce  opposite  results.     All  countries  in  the  torrid  zone 
are  not  hot,  and  sometimes  we  find  places  at  high  elevation 
which  are  not  very  cold.     But  by  a  careful  consideration 
of  the  circumstances  it  can  usually  be  found  out  how  to 
account  for  any  climate. 

THE   ATMOSPHEKE. 

535.  Weight  of  the  Atmosphere. — The  barometer,  as  we 
have  seen,  indicates  the  weight  of  the  atmosphere.     If  it 
be  watched  closely,  it  will  be  seen  to  vary  slightly  through 
the  day.     By  taking  the  mean  of  several  readings  we  get 
the  average  height  for  the  day.     By  taking  the  mean  of 
these  averages  for  different  days  we  obtain  the  average  for 
the  year.     This  yearly  average  differs  at  different  places. 

536.  Variations. — The  average  for  one  month  is  not  the 
same  as  that  for  others.     It  is  usually  higher  in  winter 
than  in  summer,  and  the  variation  is  more  marked  as  we 
approach  the  equator.      The  highest  points  for  the  day 
are  about  10  A.M.  and  10  P.M.,  and  the  lowest  six  hours 
from  these.     The  daily  fluctuation  is  also  greatest  at  the 
equator. 

537.  Irregular  Changes. — But,  besides  these  periodical 
changes,  which   are  very  small,  there  are   irregular  ones, 
which  are  of  much  greater -consequence  and  magnitude. 
It  is  by  them  that  we  are  able  in  some  degree  to  predict 
the  weather.     As  vapor  of  water  is  lighter  than  air,  its  ad- 
mixture with  the  air  causes  the  mass  to  become  lighter  and 
to  produce  a  fall  of  the  barometer.   A  fall  of  the  barometer, 


METEOROLOGY.  323 


then,  usually  indicates  the  increase  of  the  amount  of  moist- 
ure in  the  air,  and,  as  such,  is  an  indication  of  rain.  The 
words  "fair,"  etc.,  printed  on  barometers,  mean  nothing, 
because  the  height  of  the  mercury  varies  with  the  locality 
and  other  things,  and  the  barometer  pointing  to  "  fair"  in 
one  place  would  in  another,  during  exactly  the  same 
weather,  point  to  "  foul."  A  sudden  descent  is  generally 
an  indication  of  an  approaching  storm,  and  a  sudden  rise, 
of  clear  weather.  But  it  must  be  borne  in  mind  that  the 
barometer  can  indicate  a  storm  only  after  the  moisture  is 
actually  in  the  atmosphere. 

538.  Uncertainty  of  Predictions  founded  on  the  Barom- 
eter.— There  are  so  many  other  causes  affecting  the  height 
of  the  barometer  besides  the  moisture  in  the  atmosphere, 
that  meteorologists  do  not  consider  that  it  alone  is  a  safe 
guide  for  the  prediction  of  storms.     The  direction  of  the 
winds  and  the  appearances  of  the  clouds  must  also  be  taken 
into  account  in  connection  with  it,  so  that,  while  it  is  not 
useless,  its  heights  are  not  considered  in  themselves  suffi- 
cient grounds  for  predicting  the  weather.     When  properly 
combined  with  other  indications  they  certainly  afford  some 
clue. 

539.  Isobaric  Lines. — If  the  heights  of  barometers  in  dif- 
ferent parts  of  the  country  are  observed  at  exactly  the 
same  time,  as  is  done  in  the  signal  stations  of  the  United 
States,  and  if  all  the  stations  which  have  the  same  baro- 
metric readings  are  connected  by  lines,  it  will  usually  be 
found  that  these  are  roughly  parallel  to  one  another,  and 
frequently  are  curves  enclosing  certain  territory  where  the 
barometer  is  highest  or  lowest.      These  lines  are  called 
isobaric  lines.     They  change  in  position  rapidly  from  time 
to  time,  and  their  changes  are  among  the  facts  relied  upon 
by  the  head  of  the  Signal  Service  Bureau  to  predict  the 
weather.     These  lines  are  shown  in  Fig.  298. 

540.  Causes  of  Changes  of  Temperature. — The   air  be- 
comes heated  because  (1)  it  absorbs  some  of  the  heat  which 


324 


NATURAL   PHILOSOPHY. 


passes  through  it  as  it  comes  from  the  sun  ;  (2)  because  it 
absorbs  heat  which  the  earth  is  radiating  into  space ;  and 
(3)  because  it  comes  in  contact  with  bodies  on  the  earth 


FIG.  298. — ISOBARIC  LINES. 

which  are  more  or  less  heated.  The  second  and  third  of 
these  causes  are  not  subject  to  any  very  sudden  variations, 
but  the  first  changes  with  all  the  positions  of  the  sun  with 
respect  to  the  observer. 

A  fourth  cause  of  change  of  temperature,  of  less  conse- 
quence, is  the  freezing  or  evaporation  of  water.  When  the 
air  is  in  such  a  dry  state  as  to  cause  much  evaporation,  the 
change  abstracts  heat  from  the  air,  and  cold  is  produced. 
When  it  is  already  charged  with  moisture,  evaporation 
ceases.  Every  one  has  experienced  how  much  hotter  the 
air  feels  when  moist.  This  is  due  to  the  fact  that  it  does 
not  evaporate  the  perspiration  of  the  body  and  so  cause 
coolness.  On  the  other  hand,  when  freezing  or  condensa- 
tion is  going  on,  heat  is,  as  it  were,  squeezed  out  of  the 
water,  and  goes  into  the  atmosphere,  raising  its  tempera- 
ture. This,  probably,  explains  why  the  Northern  hemi- 
sphere is,  on  the  average,  about  three  degrees  warmer  than 


METEOROLOGY.  325 


the  Southern.  The  great  amount  of  water  in  the  Southern 
hemisphere  makes  evaporation,  which  causes  cold. 

Clouds  at  a  small  height  above  the  earth  keep  it  from 
losing  its  heat  in  space,  so  that  cloudy  weather  is  never  the 
coldest.  In  a  similar  way,  a  sheet  or  a  newspaper  put  over 
a  plant  will  protect  it  in  frosty  weather  by  retaining  its  own 
warmth  and  that  of  the  earth. 

Our  clothing  is  as  much  for  the  purpose  of  keeping  in 
the  heat  of  the  body  as  of  keeping  out  the  cold  of  winter. 

541.  Effect  of  Clouds.—"  The  temperature  varies  much 
less  over  cloudy  than  over  clear  districts ;  it  varies  less  in 
low  than  in  elevated  regions ;  it  is  warmer  on  one  side  of 
an  area  of  high  or  low  pressure  than  on  the  other,  and  gen- 
erally warmer  in  advance  of  any  storm-centre  and  colder 
in  the  rear."  l 

542.  Hottest  and  Coldest  Months. — The  hottest  month  in 
the  year  is  August,  and  the  coldest  is  January.     These  do 
not  coincide  with  the  times  when  the  sun  is  at  his  position 
of  greatest  and  least  power,  which  are  about  the  20th  of 
June  and  the  20th  of  December.     But  for  some  time  after 
the  20th  of  December  the  earth  is  still  radiating  heat  more 
rapidly  than  it  is  taking  it  in,  and  hence  continues  to  grow 
cooler ;  and  for  some  time  after  the  20th  of  June  the  earth 
receives  more  heat  than  it  radiates,  and  so  continues  to 
grow  hotter. 

For  the  same  reasons  the  highest  daily  temperature 
occurs,  on  the  average,  at  2  P.M.,  and  the  lowest  at  4  A.M. 

543.  Position  of  Thermometer. — By  the  temperature  of 
the  atmosphere  we  mean  the  temperature  in  the  shade.   A 
thermometer  to  record  this  should,  therefore,  be  protected 
from  the  direct  rays  of  the  sun,  and  from  radiation  from 
walls  and  other  bodies  liable  to  become  heated. 

544.  Isothermal  Lines. — If  all  the  places  on  the  earth 
having  the  same  mean  annual  temperature  be  joined,  these 


1  Circular  of  the  Signal  Bureau,  U.S.A. 
28 


326 


NATURAL  PHILOSOPHY. 


METEOROLOGY.  327 


lines  are  called  isothermal  lines.  Roughly  speaking,  they 
are  parallel  with  the  equator,  and  agree  with  parallels  of 
latitude.  But  local  circumstances  affect  this  considerably. 
Fig.  299  shows  the  isothermal  lines.  The  figures  on  them 
give  the  mean  temperature  for  the  year  of  all  the  points 
through  which  they  pass.  It  will  be  observed  how  the 
Gulf  Stream  deflects  the  lines  to  the  north  by  raising  the 
temperature  of  the  Atlantic  Ocean,  and  how  the  warm  air 
from  the  Pacific  raises  the  temperature  of  the  Western 
United  States. 

545.  Moisture  in  the  Atmosphere. — The  air  is  porous,  and 
particles  of  vapor  of  water  occupy  these  pores.     When 
heated,  the  air  expands,  and  the  pores  are  enlarged,  so  that 
more  room  exists  for  vapor.     When  the  pores  are  full  of 
moisture,  the  air  is  said  to  be  saturated.   If  the  temperature 
is  raised,  the  same  air  is  not  saturated ;  if  it  is  lowered, 
some  of  the  moisture  is  squeezed  out,  and  shows  itself  as 
mist,  dew.  frost,  rain,  hail,  snow,  or  clouds. 

546.  Relative  Humidity. — The  capacity  of  the  air  to  hold 
water,  then,  depends  on   its   temperature.     The  absolute 
amount  of  moisture  is  not   measured  by  meteorologists, 
only  the  percentage  of  full  saturation.     This  is  called  the 
relative  humidity.   If  the  air  is  just  half  full  of  moisture,  the 
relative  humidity  is  50 ;  if  full,  100 ;  if  absolutely  dry,  0 ; 
but  if,  while  the  amount  of  moisture  remains  the  same,  the 
temperature  is  raised,  the  relative  humidity  is  lowered. 

547.  Dew-Point. — If  a  certain  amount  of  moisture  exists 
in  the  atmosphere,  the  air  can  be  cooled  down  to  such  a 
temperature  that  it  will  be  saturated.     This  temperature  is 
the  dew-point.     It  is  not  uniform,  but  varies  with  the  hu- 
midity and  temperature  of  the  air.     The  air  is  usually  not 
fully  saturated  with  moisture  at  the  temperature  which 
exists.     The  dew-point  in  ordinary  clear  weather  is  about 
10°  below  the  actual  temperature,  and  in  exceptionally  dry 
times  it  is  as  much  as  30°  below  in  this  climate.     By  this 
we  mean  that  ordinary  air  must  be  diminished  in  temper- 


328 


NATURAL   PHILOSOPHY. 


ature  10°  before  it  will  be  saturated  and  dew  or  clouds 
will  begin  to  form. 

548.  Hygrometer. — The  relative  humidity  of  the  air  is 
determined  by  an  instrument  called  the  hygrometer. 

Experiment   185. — Buy  two  thermometers  and  place  them  side  by 
/ijSijjj,K  side.     Wrap  the  bulb  of  one  in  a  can- 

dle-wick, which  passes  down  into  a 
vessel  of  water  so  close  that  the  wick 
around  the  bulb  will  always  be  wet. 
The  "  wet-bulb  thermometer"  will  show 
a  lower  temperature  than  the  u  dry-bulb 
thermometer,"  for  evaporation  from  the 
wick  cools  the  bulb  and  the  mercury  in 
the  tube.  The  amount  of  this  evapora- 
tion will  depend  on  the  dryness  of  the 
air.  If  it  is  saturated,  there  will  be  no 
evaporation,  and  the  two  thermometers 
will  register  the  same.  If  the  air  is 
very  dry,  much  evaporation  will  result, 
and  there  will  be  a  great  difference. 
From  the  readings  of  the  two  thermom- 
eters it  is  possible  to  calculate  the  ab- 
solute amount  of  moisture  in  the  air, 
the  relative  humidity,  and  the  dew- 
point. 

549.  Variation  of   Moisture. — 

The  amount  of  vapor  in  the  at- 
mosphere varies  with  the  time  of 
day,  being  greatest  during  the 
latter  part  of  the  afternoon,  and 
least  during  the  latter  part  of  the 
night.  This  is  due  to  the  evap- 
oration which  goes  on  while  the 
sun  is  shining,  which  adds  to  the 
moisture  in  the  air  through  the 

day,  and  to  the  condensation  of  moisture  which  results  from 
the  lowering  of  temperature  during  the  night.  For  similar 
reasons  the  amount  is  greater  in  summer  than  in  winter. 
It  is  also  greater  near  the  earth  than  in  the  higher  regions 
of  the  air,  though  no  air  has  been  found  entirely  free 
from  moisture.  Up  to  a  height  of  from  2000  to  3000  feet 
there  is,  however,  little,  if  any,  decrease  in  the  humidity. 


FIG.  300.— HYGROMETER. 


METEOROLOGY.  329 


"  There  is  an  increase  of  moisture  near  bodies  of  warm 
water,  fields  of  snow,  extensive  forests  and  meadows,  etc., 
as  compared  with  dry  plains  and  rocky  mountains.  The 
humidity  will  be  found  large  in  advance  of  storm-centres, 
and  small  in  their  rear.  It  will  be  greater  over  warm 
cloudy  districts  than  where  cold  and  clear  weather  prevails. 
Certain  winds  will  be  found  to  be  moister  than  others.  The 
west  and  northwest  are  generally  the  driest  in  the  Missis- 
sippi Valley.  Dryness  will  be  found  attending  clearing- 
up  weather.  Dampness  or  a  large  increase  of  relative 
humidity  accompanies  threatening  weather  as  an  almost 
invariable  premonition."1 

550.  Indian  Summer. — The  haziness  which  is  noticed  in 
the  atmosphere  at  certain  times,  more  particularly  during 
"  Indian  summer,"  is  largely  the  result  of  particles  of  dust 
or  charcoal  which  come  from  forest  fires,  and  which  possess 
the  property  of  attracting  moisture  and  thus  producing 
dry  weather.     A  heavy  rain  will  wash  this  out  and  leave 
the  air  clear. 

551.  Dew.— The  foliage  of  plants,  the  grass,  and  all 
things  exposed  to  the  air  at  night  quickly  lose  their  heat. 
They  cool  the  air  in  immediate  contact  with  them  below 
the  dew-point,  and,  it  being  no  longer  able  to  hold  the 
vapor,  this  is  deposited  on  the  cold  bodies.     This  is  dew. 
A  pitcher  of  ice-water  will  collect  dew  on  its  surface  from 
a  similar  cause. 

A  clear  night  favors  the  deposition  of  dew,  for  when 
clouds  are  above  the  earth  they  retain  the  heat,  so  that  the 
grass  is  not  cooled  below  the  dew-point.  A  comparatively 
still  night  favors  it,  because  in  a  strong  breeze  no  portion 
of  the  atmosphere  is  long  enough  in  contact  with  the 
bodies  to  be  sufficiently  cooled.  Great  relative  humidity 
favors  it,  for  then  the  dew-point  is  not  much  below  the 
ordinary  temperature,  and  but  little  cooling  suffices. 

1  Circular  of  Signal  Bureau,  U.S.A. 
28* 


330  NATURAL  PHILOSOPHY. 

552.  Frost. — Frost  is  frozen  vapor  or  frozen  dew.     The 
vapor  freezes  in  the  air,  and  then  settles  to  the  ground  in 
the  form  of  little  crystals.     Hence  it  is  necessary  for  the 
temperature  to  be  as  low  as  32°  at  the  place  of  freezing  in 
order  for  frost  to  be  formed.     It  is  often  cold  enough  to 
make  frost  in  the  valleys  when  the  thermometer  a  little 
higher  up  indicates  a  higher  temperature. 

553.  Fog1. — When  a  large  mass  of  air  is  cooled  below  the 
dew-point,  all  the  vapor  which  it  cannot  contain  becomes 
visible.     When  this  is  near  the  earth  it  is  called  a  fog  or 
mist.     This  cooling  may  be  the  result  of  a  cold  wind  blow- 
ing in  from  the  north  on  air  nearly  saturated,  or  of  the 
presence  of  a  bog  or  lake,  which  keeps  the  air  cool  at  a 
certain  spot.   In  the  latter  case  the  fog  is  permanent,  while 
its  particles  may  be  rapidly  changing.     As  soon  as  a  mass 
of  air  blows  into  this  position  it  is  cooled  down  so  as  to 
make  its  vapor  visible,  and  when  it  goes  out  at  the  other 
side  the  temperature  is  raised  so  that  it  hides  it  again. 
A  fog  usually  hangs  over  the  banks  of  Newfoundland, 
because  there  the  cold  and  warm  currents  meet,  and  the 
warm  air  is  cooled  below  the  dew-point.     It  is  also  seen 
over  rivers,  on  account  of  their  cooling  effect  on  the  air. 

554.  Fog,  Particles  of  Liquid. — Particles  of   vapor  are 
transparent,  and  when  they  lie  between  the  particles  of  air 
they  do  not  obstruct  the  view.     When,  however,  they  are 
not  thus  placed,  they  collect  in  little  drops,  which  float  in 
the  air  and  obstruct  the  view,  because  the  light-rays  are 
lost  by  their  numerous  reflections  from  one  to  the  other. 
In  the  same  way  glass  is  transparent,  but  a  vessel  filled 
with  broken  glass  is  opaque.     In  the  condensation  which 
occurs  when  fog  is  formed,  the  vapor  changes  from  a  gase- 
ous body  to  a  liquid  body.     The  change  may  be  seen  at  the 
spout  of  a  tea-kettle.     Close  to  the  orifice  nothing  is  seen, 
for  the  steam  is  a  transparent  gas.     When  it  goes  out  a 
little  space  it  is   cooled  below  the  dew-point,  and  liquid 
vapor  of  water  becomes  visible. 


METEOROLOGY.  331 


555.  Cloud. — When   this   condensation   goes   on   in  the 
upper  regions  of  the  atmosphere,  a  cloud  is  formed.   A  cloud 
is  simply  a  fog  or  mist  at  some  elevation  above  the  earth. 
When  we  ascend  a  mountain  we  often  enter  a  cloud,  and  no 
distinction  from  a  mist  is  noticed.     Clouds  are  apt  to  hang 
around  mountain-tops,  for  the  cold  peaks  lower  the  temper- 
ature of  the  air,  and  as  fast  as  it  rises  to  pass  over  them  it 
is  cooled  below  the  dew-point.     When  it  descends  the  op- 
posite side  it  becomes  warm  again,  and  the  cloud  disappears 
from  view.     While  the  cloud  apparently  remains  fixed  in 
position,  its  particles  are  constantly  changing. 

556.  Causes  of  Clouds. — A  cloud  may  also  be  formed  by 
a  cold  wind  blowing  on  warmer   air,  or  by  warmer  air 
blowing  into  a  colder  region,  or  by  an  ascending  current 
of  air  expanding  and   so  causing  cold  (Art.  367).     The 
latter  cause  is  probably  the  most  common.     The  vapor 
formed  by  the  action  of  the  sun  upon  the  waters  of  the 
earth  tends  by  its  own  expansive  force  to  rise  above  the 
earth ;  as  it  rises  it  reaches  rarer  strata  of  air,  and  so  ex- 
pands more  rapidly.     This  expansion  causes  cold,  and,  be- 
sides this,  the  air  itself  is  colder  as  we  rise  higher.     The 
vapor  is  then  changed  from  invisible  vapor  to  the  little 
particles  of  water  which  constitute  cloud. 

"  557.  Forms  of  Clouds. — As  the  cloud-particles  are  heavier 
than  the  air,  they  gradually  sink.  They  would  fall  to  the 
ground  did  they  not  come  into  warmer  air,  by  which  they 
are  again  converted  into  invisible  vapor.  As  soon  as  they 
get  down  to  a  stratum  which  raises  their  temperature 
above  the  dew-point,  they  disappear  from  view.  This  ex- 
plains why  certain  clouds  have  flat  bases  while  their  tops 
are  heaped  up  in  masses  like  mountains.  This  form  of 
cloud  has  often  great  thickness.  The  bottom  may  not 
be  over  a  half-mile  from  the  earth,  but  the  top  sometimes 
reaches  the  height  of  four  miles.  In  general,  the  thickness 
of  clouds  is  not  more  than  a  half-mile,  and  they  vary  from 
a  half-mile  to  five  miles  above  the  surface  of  the  earth. 


332  NATURAL   PHILOSOPHY. 


There  is  frequently  just  as  much  vapor  below  the  cloud 
as  in  them,  but  the  warmer  temperature  prevents  it  from 
being  seen. 

Questions. — When  you  build  a  fire  in  a  damp  room,  do  you  de- 
crease the  amount  of  moisture  in  the  room?  Why  is  the  room 
drier  ?  Is  it  the  visible  or  the  invisible  vapor  that  gives  the  idea  of 
dampness  ? 

558.  Classes  of  Clouds. — Clouds  are  usually  divided  into 
four  main  classes, — cirrus,  cumulus,  stratus,  and  nimbus. 

559.  Cirrus. — The  cirrus  clouds  are  the  light,  feathery 
masses  which  float  in  the  air,  scarcely  screening  the  sun. 
They  are  believed  to  be  composed  of  small  particles  of  ice 
or  snow  floating  at  a  great   height.     They  sometimes  be- 
token the  coming  of  a  storm,  though  usually  nothing  ever 
falls  from  them. 

560.  Cumulus. — The  cumulus  or  "  heap"  clouds  are  clouds 
which  are  common  in  summer-time  in  fair  weather.     They 
are  the  clouds  with  flat  bases  and  hemispherical  tops,  men- 
tioned in  Paragraph  557.     They  are  the  tops  of  columns  of 
vapor  reaching  down  to  the  earth  which  become  visible  at 
a  height  where  the  temperature  falls  below  the  dew-point. 
The  shapes  of  these  clouds  are  best  seen  through  a  piece 
of  blue  glass,  which  diminishes  some  of  the  glare  of  their 
light. 

561.  Stratus. — The  stratus   clouds  are  those  which  are 
seen  in  lines  stretched  along  parallel  to  the  horizon.   When 
overhead,  they  cover  the  sky  with  a  cloud  of  uniform  dark- 
ness.    They  are  near  the  earth,  and  of  no  great  thickness. 

562.  Nimbus. — The  nimbus  are  heavy  black  clouds,  from 
which  rain  falls. 

563.  Mixed  Classes. — There  are  often  observed   clouds 
which  partake  of  the  character  of  two  or  more  kinds  ; 
these  are  named  cirro-stratus,  cumulo-stratus,  etc. 

564.  Disappearance  of  Clouds. — Clouds  form  and  disap- 
pear in  the  sky  while  we  are  looking  at  them.     The  clear- 
ing up  after  a  storm  is  not  so  much  the  result  of  the  clouds 


METEOROLOGY.  333 


blowing  away  as  of  their  disappearance  by  being  changed 
to  invisible  vapor  by  a  drier  atmosphere. 

565.  Clouds  around  a  Storm. — "  Two  or  more  layers  of 
clouds  almost  invariably  coexist  wherever  extended  rain- 
storms prevail,  the  upper  layer  stretching  far  in  advance 
of  the  lower,  but  stretching  down  to  it  where  rain  is  falling 
most  abundantly.     In  the  rear  of  this  area  cumulus  clouds 
are  abundant.     Cumulus  and  cirrus  clouds  are  not  incon- 
sistent with  the  idea  of  clear  or  fair  weather.     Cirro-stratus 
almost  invariably  precede  an  extensive  rain-storm,  whether 
in  winter  or  summer.     The  stratus  will  generally  be  found 
in  connection  with  threatening  weather." l 

566.  Rain. — When  the  air  is  suddenly  cooled  below  the 
dew-point,  the   little  particles  collect  in   drops,  and  rain 
is  formed.     This  sudden  cooling  is  most  readily  effected  by 
an  upward  current,  which  carries  air  nearly  saturated  to  a 
cooler  level.     There  is  a  difference  of  about  35°  between 
the  air  at  the  surface  and  the  air  two  miles  above  the  sur- 
face of  the  earth.     When  the  air  laden  with  moisture  from 
the  ocean  is  carried  landward  and  over  a  mountain-top,  we 
usually  have  copious  rains.     Another  cause  is  the  mixing 
of  two  clouds  or  two  masses  of  air  of  different  tempera- 
tures.    If  you  mix  a  cubic  foot  of  saturated  air  at  90°  and 
another  at  30°  they  will  have  a  mean  temperature  of  60° ; 
but  air  at  this  temperature  will  not  hold  all  the  moisture . 
of  both  masses,  and  some  must  fall  as  rain. 

567.  Amount  of  Rainfall. — More  rain  falls  at  the  equator 
than  elsewhere,  and  the  decrease  is  quite  uniform  to  the 
poles.     About  100  inches  of  rain  fall  at  the  equator  an- 
nually.    By  this  we  mean  that  if  all  of  it  could  be  collected 
it  would  cover  the  surface  to  a  depth  of  100  inches.   In  our 
latitude  the  average  rainfall  is  between  30  and  40  inches. 

568.  Snow. — When  the  vapor  of  the  air  is  frozen,  snow 
is  formed.     Freezing  is  a  form  of  crystallization,  and  the 

1  Circular  of  Signal  Bureau,  U.S.A. 


334 


NATURAL   PHILOSOPHY. 


forms  of  the  crystals  of  snow  are  very  beautiful.  To  ob- 
serve them  well,  let  them  fall  on  cold  pieces  of  colored 
glass  and  examine  them  with  a  microscope  of  low  power. 

Do  not  breathe  on  them. 


FIG.  301. — FORMS  OF  SNOW-CRYSTALS. 

Prof.  Tyndall  speaks  of  the  snow-crystals  which  he  saw 
on  Monte  Rosa  as  "  a  shower  of  frozen  flowers ;  all  of  them 
were  six-leaved ;  some  of  the  leaves  threw  out  lateral  ribs 
like  ferns  ;  some  were  rounded,  others  arrowy  and  serrated ; 
but  there  was  no  deviation  from  the  six-leaved  type." 
.  569.  Hail. — Hail  is  frozen  water.  It  is  produced  during 
thunder-storms  by  the  approach  of  a 
cold  current,  which  forces  upward  the 
warm,  saturated  air  of  the  lower  re- 
gions. Snow  is  first  formed,  and  the 
whirling  action  of  the  air  collects  this 
into  little  balls,  which,  as  they  move 
through  the  snow  and  vapor,  become 
alternately  coated  with  snow  and  cov- 
ered with  ice,  gradually  but  rapidly 
growing  till  they  reach  sometimes  the  size  of  turkey- 
eggs.  When  examined,  the  centre  is  seen  to  consist  of 


FIG.  302. — SECTION  OF 
HAIL-STONE. 


METEOROLOGY. 


335 


snow,  and  often  alternate  layers  of  snow  and  ice  may  be 
noticed. 

570.  Wind, — Wind  is  air  in  motion.  Air  having  mass, 
when  it  strikes  any  object  it  presses  against  it,  the  pressure 
being  harder  the  faster  it  moves.  A  wind  moving  at  the 
rate  of  4  miles  an  hour  is  a  pleasant  breeze,  and  presses 
against  every  square  foot  of  surface  which  it  strikes  verti- 
cally with  a  force  of  about  an  ounce.  A  brisk  wind  of  25 
miles  per  hour  has  a  force  of  about  3  pounds  per  square 
foot;  a  very  high  wind  of  45  miles  per  hour,  of  10  pounds 
per  square  foot ;  a  hurricane  of  80  miles  per  hour,  of  31 
pounds  "per  square  foot. 

The  mean  velocity  of  the  wind  in  the  Eastern  United 
States  is  about  10  or  12  miles  per  hour,  being  more  in 
winter  than  in  summer,  and  is  greatest  at  2  P.M.,  and  least 
at  night.  The  daily  curve  is  seen  in  Fig.  303. 


10  noon.2h.    *      6      a     1O  xat 

FIG.  303.  —  DAILY  CURVE  OF  WIND. 


571.  Cause  of  Winds.  —  The  air  at  the  equator  is  heated 
by  the  direct  rays  of  the  sun,  and  is  pushed  up  by  the 
heavier  cold  winds  from  the  polar  regions  settling  down  to 
take  its  place.  The  heated  air  moves  as  an  upper  current 
towards  the  poles,  while  the  cold  air  moves  as  a  surface- 
current  towards  the  equator.  This  interchange  would  go 
on  regularly  and  continually  were  it  not  for  the  rotation 
of  the  earth  on  its  axis.  A  particle  at  the  equator  moves 
with  greater  velocity  than  one  near  the  poles,  because  it 
has  so  much  farther  to  go  in  the  same  time.  The  air  par- 
takes of  the  motion  of  the  earth  below  it,  and  when  the 
slowly-moving  air  from  the  higher  latitudes  sweeps  down 
towards  the  equator  it  is  left  behind  and  falls  back  towards 


336 


NATURAL   PHILOSOPHY. 


the  west.  This  produces  the  trade-winds  of  the  torrid 
zone.  When  the  upper  currents  from  the  equator  reach 
the  temperate  zones  they  become  sufficiently  cooled  to  fall 
again  to  the  surface,  and,  having  the  rapid  equatorial 
motion,  they  sweep  ahead  of  the  earth  and  form  the  pre- 
vailing westerly  winds  of  our  latitude. 

The  extreme  cold  of  the  polar  regions  produces  surface- 
currents  away  from  the  poles  and  upper  currents  towards 
them. 


FIG.  304. — WINDS  OVER  THE  GLOBE. 

The  surface-winds  are  shown  in  Fig.  304,  and  Fig.  305 
gives  the  whole  circulation  without  the  effects  of  the  earth's 
rotation. 

572.  Variable  Winds. — These  are  the  general  systems  of 
winds.  But,  as  every  one  knows,  the  changes  in  direction 
and  intensity  of  the  wind  are  almost  continuous.  There 
are  numerous  local  circumstances  which  determine  par- 
ticular winds.  Wherever  there  is  low  pressure,  as  indi- 
cated by  the  barometer,  there  are  surface-currents  sweep- 
ing in  from  all  around,  for  the  equilibrium  of  the  atmosphere 
is  destroyed  and  a  flow  sets  in  to  restore  it.  If  any  place 


METEOROLOGY. 


337 


becomes  greatly  heated,  the  air  will  tend  to  flow  into  it 
in  all  directions,  producing  surface-currents  towards,  and 
upper  currents  away  from,  the 
heated  place.  When  the  heated 
air  rises,  it  becomes  cooled, 
spreads  out,  and  falls  down, 
and  is  returned  again  to  the 
place  whence  it  came. 

The  reverse  would  take  place 
around  a  cold  centre. 

573.  Land  and  Sea  Breezes. — 
During  the  day  the  land  heats 
up  more  than  the  water,  so  that 
along  the  sea-coast  there  are 
usually  breezes  blowing  in  from 
the   sea  during  the  day.     At 
night   it   loses   its   heat  more 
quickly    and    becomes    cooler 
than  the  sea,  so  that  the  breeze 
sets  in  in  the  opposite  direc- 
tion. 

574.  Monsoons. — The  same  cause  produces  the  monsoons 
of  the  Indian  Ocean.     The  regions  of  India  become  heated 
in  their  summer,  and  the  wind  sets  in  strongly  from  the 
Indian  Ocean.     In  the  winter  the  reverse  is  the  case. 

575.  Moisture  a  Cause  of  Winds, — Another  local  cause 
of  winds  is  the  moisture  in  the  atmosphere.     As  vapor  of 
water  is  lighter  than  air,  the   sudden  formation  of  cloud 
will  tend  to  produce  a  low  barometer.     Winds  will  set  in 
towards  this  centre  to  restore  the  equilibrium. 

576.  Difficulty  in  ascertaining  the   Cause  of  Winds,— 
Among  all  these  causes  it  is  often  impossible  to  say  which 
one  is  producing  the  wind  at  a  given  time  and  place.     Its 
fickleness  has  become  proverbial,  and  many  causes  doubt- 
less operate  together  in  producing  the  modifications.     The 
changes  are  not  the  result  of  chance,  but  every  particle  of 


FIG.  305.— CIRCULATION  IN  THE  AIR. 


338  NATURAL   PHILOSOPHY. 

air  moves  in  obedience  to  the  impulses  which  act  upon  it. 
Winds  are  great  agents  for  purifying  the  earth  and  making 
it  healthy,  and  a  multitude  of  ways  in  which  they  are 
useful  to  man  will  suggest  themselves  to  any  one. 

577.  Storm. — A  storm  is  a  great  commotion  in  the  atmos- 
phere.    Eain,  hail,  or  snow  generally  accompanies  it. 

578.  Effect  of  Heat. — In  case  of  the  heating  of  a  large 
tract,  the  cold  air  flows  in  from  all  around.     The  hot  air 
rises  and  spreads  out.     This  mingling  of  the  currents  often 
produces  clouds  and  rain,  as  has  been  explained.     This 
is  a  storm.     The. whole  system  of  currents  and  clouds  is 
then  carried  by  the  prevailing  winds  over  the  country.     A 
barometer  near  the  centre  would  show  low  pressure. 

579.  Effect  of  Rotation  of  the  Earth. — Were  there  no  ro- 
tation of  the  earth,  the  surface-air  would  always  blow  di- 
rectly towards  the  storm-centre,  and  the  upper  air  away. 
In  the  Northern  hemisphere  the  winds  coming  in  from  the 
south  are,  by  their  more  rapid  motion  with  the  earth  around 
its  axis,  carried  towards  the  east,  and  those  coming  in  from 
the  north  are  in  like  manner  deflected  towards  the  west. 
This  makes  them  approach  the  centre  not  directly,  but  in 
a  spiral  curve,  and  creates  a  "cyclone."     Nearly  all  our 
storms  are  more  or  less  cyclonic  in  their  character.     The 
reverse  kind  of  cyclone  exists  in  the  Southern  hemisphere. 

580.  Movement  of  Storms. — The  prevailing  winds  in  the 
torrid  zone  being  easterly,  the  storm  is  carried  towards  the 
west.     As  it  recedes  from  the  equator  it  reaches  the  region 
of  westerly  winds,  by  which  it  is  borne  eastward.     Most 
of  our  large  storms  come  from  the  west  or  the  southwest. 

This  may  not  be  the  direction  of  the  wind  at  the  time. 
The  wind  at  any  time  is  usually  directed  obliquely  towards 
the  storm-centre,  and  this  is  frequently  modified  by  local 
causes,  so  that  there  are  all  possible  directions  inside  the 
storm-area.  In  the  Atlantic  States  the  winds  commonly 
blow  from  some  easterly  quarter  during  a  storm. 

581.  Storm-Centre. — In  the  centre  of  a  storm  there  is  a 


METEOROLOGY. 


339 


calm,  and  sometimes  clear  weather.  After  the  centre  has 
passed,  the  wind  shifts  to  the  west,  it  often  rains  hard  for  a 
short  time,  and  then  clears  away.  When  the  wind  shifts 


FIG.  306.— MOTION  OF  STORM-CENTRE  AND  OF  AIR  AROUND  IT. 

to  the  west  after  several  days  of  east  wind,  clear  weather 
soon  follows. 

582.  Direction  of  Wind  around  a  Storm-Centre. — To  re- 
member the  direction  of  the  surface-winds  around  a  storm- 
centre,  the  student  may  notice  that  in  the  Northern  hemi- 
sphere, to  a  person  situated  above,  the  motion  is  opposite 
to  that  of  the  hands  of  a  watch. 

583.  Direction  of    Storms, —  The   direction   of    storms 
through  the  United  States  is  towards  the  east,  varying 
sometimes  to  the  northeast  or  the  southeast,  and  their  aver- 
age hourly  rate  of  motion  is  21  miles  in  summer  and  30  in 
winter.     They  sometimes  move  faster  than  this,  and  some- 
times remain  almost  stationary. 

584.  Thunder-Storms, — The  storms  of  wind  and  rain  of 
summer,  often  accompanied  by  thunder  and  lightning,  do 
not  move  across  the  continent,  but  are  local  in  their  origin. 


340 


NATURAL   PHILOSOPHY. 


The  heat  of  the  sun  fills  the  lower  regions  with  vapor  over 
some  point,  and  causes  it  to  ascend  till  its  cooling  produces 
cumulus  clouds  level  at  base,  heaped  up  on  top.  This  goes 
on  till  condensation  into  drops  ensues  and  rain  falls.  The 
winds  sweep  the  clouds  along,  and  there  is  a  certain 
amount  of  cyclonic  tendency,  but  the  storm  does  not  ex- 
tend far,  and  is  soon  exhausted.  The  electric  phenomena 
accompanying  such  storms  have  been  explained  in  the 
chapter  on  electricity. 

585.  Cyclones. — Frequently  cyclones  or  hurricanes  are 
formed  in  the  Atlantic  Ocean,  near  the  equator,  and  are 
swept  along  westward,  as  shown  in  Fig.  307,  then  turn 


FIG.  307. — COURSE  OF  CYCLONES  IN  THE  ATLANTIC  OCEAN. 

opposite  the  South  Atlantic  States,  and  are  usually  lost  in 
the  North  Atlantic,  though  they  sometimes  doubtless  reach 
Europe.  In  this  case,  as  the  storm-centre  sweeps  up  the 
course  of  the  Gulf  Stream,  we  have  east  and  southeast 
winds  along  our  eastern  coast,  accompanied  by  heavy  rain. 


METEOROLOGY.  341 


The  eastern  storms  which  begin  at  the  South  are  usually 
of  this  class.  Occasionally  the  storm  does  not  turn  till  it 
reaches  the  Gulf  of  Mexico,  when  it  moves  centrally  across 
the  United  States. 

In  the  equatorial  regions  the  cyclones  are  more  violent, 
the  rain  is  more  extensive,  and  the  wind  is  stronger  than  in 
the  temperate  zones.  The  energy  is  somewhat  diminished 
by  the  distance  travelled. 

586.  Prediction  of  Storms— Signal  Bureau. — The  laws 
governing  the  motions  of  storms  are  now  so  well  estab- 
lished that  it  is  possible  to  predict  with  tolerable  certainty 
for  one  or  two  days  in  advance  what  the  weather  will  be. 
This  is  the  work  of  the  Signal  Service  Bureau  of  the  War 
Department  of  the  United  States  Government.  There  are 
scattered  over  the  country  about  one  hundred  stations,  at 
each  of  which,  three  times  every  day,  at  the  same  instant 
of  actual  time,  observations  are  taken  by  the  officer  in 
charge.  These  are  telegraphed  immediately  to  the  chief 
signal  officer  at  Washington,  who  in  turn  telegraphs  many 
of  them  to  some  of  the  more  important  stations,  from  which 
bulletins  of  the  prominent  features  are  issued.  These  bul- 
letins tell — 

Height  of  the  barometer ; 

Change  since  last  report ; 

Thermometer ; 

Change  in  the  last  twenty-four  hours ; 

Relative  humidity ; 

Direction  of  the  wind ; 

Velocity  of  the  wind ; 

Force  of  the  wind  ; 

Amount  of  cloud; 

Rainfall  since  last  report ; 

State  of  the  weather. 

These  bulletins  are  open  to  examination  at  the  signal- 
offices  and  other  public  places  in  the  cities  and  towns  to 
which  they  are  transmitted. 

29* 


342  NATURAL   PHILOSOPHY. 


Besides  the  bulletins,  a  statement  of  synopses  and  indi- 
cations is  prepared  at  the  office  of  the  chief  signal  officer, 
and  thence  issued  thrice  daily.  The  press  agents  telegraph 
it  over  the  country.  This  statement  is  given  out  at  1  A.M., 
10  A.M.,  and  7  P.M.  daily,  Washington  time. 

587.  Correctness  of  the  Indications.— The  indications 
nearly  always  prove  correct.     The  signal  officer  receives 
reports  of  storms,  or  cold  waves,  or  clearing  weather,  from 
the  West,  and  their  rate  of  travel,  from  which  he  has  to 
predict  where  they  will  be  at  a  given  time.    It  is  not  always 
a  simple  matter.     He  has  to  take  into  account  a  variety  of 
possible  modifying  circumstances,  and  great  study  and  ex- 
perience are  needed  to  make  it  right  in  nine  cases  out  of 
ten,  which  is  about  the  record  of  our  bureau.     JSTo  other 
nation  has  so  complete  or  well-arranged  a  system  as  ours, 
and  it  is  well  worth  all  it  costs.     Many  vessels  are  pro- 
tected from  wreck  by  heeding  the  signals  of  a  coming 
storm  which  are  displayed  along  the  coast,  and  the  dwellers 
along  the  Western  rivers  are  often  saved  from  floods  by 
timely  notice  of  their  approach. 

588.  Weather  Chart. — The  chief  signal  officer  also  issues, 
thrice  daily,  a  graphic  weather  chart,  which  shows  at  a 
glance  the   weather  all  over  the  country  at  that  hour. 
Any  one,  with  proper  care  and  knowledge,  can  forecast 
the  weather  for  himself  by  a  study  of  these  charts. 


APPENDIX   I. 


THE  METEIC   SYSTEM. 

THE  metric  system  of  weights  and  measures  was  devised  in  France 
about  the  beginning  of  the  present  centu^.  It  is  now  in  general 
use  in  most  of  the  countries  of  the  civilized  world,  and  in  the  others 
is  largely  used  in  scientific  work. 

The  unit  of  length  in  this  system  is  the  metre,  which  is  equivalent 
to  39.37  inches.  This  was  taken  because  it  is  one  ten-millionth  of 
the  distance  from  the  earth's  equator  to  the  pole.1  On  account  of  its 
great  convenience,  the  system  was  made  decimal  throughout.  The 
prefixes  to  denote  the  fractions  of  a  unit  are  the  Latin  numerals,  and 
are  the  same  for  all  the  tables,  while  the  Greek  numerals  indicate 
the  multiples  of  the  unit  in  all  the  tables. 


TABLE   OF   MEASUKES   OF   LENGTH. 

SYMBOL. 

METRIC  VALUE. 

U.  S.  VALUE. 

1  millimetre, 

mm. 

.001  m. 

.03937  in. 

10  millimetres 

=  1  centimetre, 

cm. 

.01  m. 

.3937  in. 

10  centimetres 

=  1  decimetre, 

dm. 

.1  m. 

3.937  in. 

10  decimetres 

=  1  metre, 

m. 

1  m. 

39.37  in. 

10  metres 

=  1  dekametre, 

Dm. 

10m. 

32.81  ft. 

10  dekametres 

=  1  hectometre, 

Hm. 

100m. 

19.92  rd. 

10  hectometres 

=  1  kilometre, 

Km. 

1,000  m. 

.6214  mi. 

10  kilometres 

=  1  myriametre, 

Mm. 

10,000  m. 

6.214  mi. 

The  unit  of  capacity  is  the  litre  (lee'ter) ;  it  is  the  quantity  which 
a  cubical  box,  1  decimetre  each  way  inside,  will  hold.  It  is  equiva- 
lent to  1.0567  quarts  liquid  measure,  or  .908  quart  dry  measure,  so 
that  it  is  between  our  dry  and  liquid  quarts,  and  does  not  differ 


*  The  more  accurate  measurements  of  recent  years  have  shown  that  the  standard 
metre  which  the  French  adopted,  and  which  is  still  used  everywhere,  is  a  trifle  (53^3) 
shorter  than  an  exact  ten-millionth  of  this  distance. 

343 


344  APPENDIX. 


greatly  from  either.  The  same  measures  are  used  for  both  liquid  and 
dry  measure.  The  table  of  measures  of  capacity  is  exactly  the  same 
as  the  one  for  length  given  above,  except  that  metre  is  changed  to 
litre.  Its  symbol  is  I. 

The  unit  of  weight  is  the  gram ;  it  is  the  weight  of  pure  water  at 
39°  F.  which  a  cubical  box,  1  centimetre  each  way  inside,  will  hold. 
It  is  equivalent  to  15.432  grains ;  a  five-cent  piece  weighs  5  grams 
and  is  2  centimetres  in  diameter.  The  table  is  made  in  the  same  way 
as  before,  by  changing  metre  to  gram,  in  the  table  given  above. 
Its  symbol  is  g. 

In  measuring  surfaces  the  square  metre,  square  dekametre,  etc., 
are  used.  The  are  (air),  which  is  a  square  dekametre,  is  also  used, 
and  a  table  is  made  by  using  it  with  the  common  prefixes. 

Cubic  decimetres,  cubic  metres,  etc.,  are  also  used  in  measuring 
solids,  as  well  as  the  stere  (stair),  which  is  a  cubic  metre.  Its  table 
is  made  in  the  same  way  as  the  others. 


APPENDIX    II. 


A  TABLE   OF   SPECIFIC   GEAYITIES. 


LIQUIDS. 


Pure  water,  at  39°  F 1.000 

Sea-water 1.026 

Alcohol 791  to  .916 

Ether 716 


Sulphuric  Acid 1.841 

Milk 1.032 

Mercury,  at  32°  F 13.596 


SOLIDS. 


Iridium  23 

Platinum  ..  21  to  22 

Gold  19  to  19.6 

Lead 11.4 

Silver 10.5 

Copper 8.6  to  8.9 

Brass 7.8  to  8.5 

Iron,  cast 7  to  7.3 

"      wrought 7.6  to  7.8 

Steel 7.8 

Glass ,. 2.5  to  3 

Quartz  .....' 2.65 


Brick 2  to  2.17 

Chalk 1.8  to  2.8 

Coal,  bituminous 1.02  to  1.35 

"      anthracite 1.36  to  1.85 

Limestone 2.4  to  3. 

Ice 93 

Wood,  lignum-vitae 1.34 

"       hickory 83  to  1. 

"       oak 85 

"       pine 42  to  .55 

"       cork 24 


GASES. 

Air 1.  [Hydrogen. 

Oxygen 1.11  | 


.07 


346 


INDEX. 


[THE  NUMBERS  REFER  TO  PAGES.] 


Aberration,  spherical,  187. 
Adhesion,  definition  of,  14. 
Affinity,  definition  of,  13. 
Air-Brake,  111. 
Air-Condenser,  110. 

experiments  with,  111. 
Air-Pump,  104. 

experiments  with,  107. 
Alarm-Bell,  303. 
Aneroid  Barometer,  99. 
Artesian  Wells,  73. 
Atmosphere,  100,  322. 

composition  of,  100. 

height  of,  100. 

weight  of,  100,  322. 

buoyancy  of,  102. 

moisture  in,  328. 
Atoms,  8. 
Attraction,  electrical,  261. 

definition  of,  13. 


Balance  a  lever  of  the  first  kind,  49. 
Balloons,  102. 
Barker's  Mill,  92. 
Barometer,  97. 

and  the  weather,  98,  323. 
Battery,  281. 
Beats  in  sound,  155. 
Bellows,  103. 
Boiling  Point  and  pressure,  228. 


Cabinet-Organ,  141. 
Cables,  298. 
Camera,  209. 


Capillary  Attraction,  14,  80. 

repulsion,  81. 
Centre  of  gravity,  36. 

Centrifugal  Force,  28. 

Character  of  sound,  147. 

Clarionet,  142. 

Clepsydra,  84. 

Climate,  causes  of,  319. 

Clocks,  use  of  pendulum  in,  46. 

Clouds,  331. 

classes  of,  332. 

Cohesion,  definition  of,  13. 

Colors,  primary,  199. 
complementary,  199. 

Compass,  253. 

Complementary  Colors,  199. 

Composition  of  forces,  26. 

Conduction  of  heat,  234. 
Conductors  of  electricity,  259. 
Conservation  of  energy,  33,  216. 
Convection  of  heat,  236. 
Cornet,  142. 

Correlation  of  forces,  34. 
Cryophorus,  225. 
Cupping,  101. 
Cyclones,  340. 

D. 

Declination  of  the  compass,  253. 

Dew,  cause,  329. 

Dew-Point,  327. 

Diamond  the  hardest  of  substances,  12. 

Dip  of  the  compass,  253. 

Discord  in  sound,  156. 

Dispersion  of  light,  188. 

Distillation,  229. 

Dynamo-Electric  machines,  306. 

Dynamometer,  22. 

Dyne,  the  unit  of  force,  22. 

347 


348 


INDEX. 


E. 

Ear,  158. 

Ear-Trumpets,  125. 
Echoes,  126. 
Elasticity,  cause  of,  11. 

of  liquids,  64. 
Electrical  Machines,  263. 
Electric  Light,  283,  308. 
Electricity,  chapter  on,  256. 

two  kinds  of,  257. 

frictional,  255. 

current  or  voltaic,  277. 
Electrolysis,  285. 
Electro-Magnetism,  289. 
Electrophorus,  267. 
Electro-Plating,  285. 
Elements,  number  known,  9. 
Energy,  definition  of,  32,  34. 

potential  energy,  32. 

actual  energy,  32. 

conservation  of  energy,  33. 
Erg,  a  unit  of  work,  31. 
Ether  pervades  all  matter  and  space,  16. 

probably  a  form  of  radiant  matter,  17. 
Evaporation,  220,  225,  227. 
Expansion  by  heat,  10,  221. 

by  cold,  10,  226. 
Eye,  209. 

F. 

Falling  Bodies,  laws  of,  40,  41. 
Fife,  142. 
Fire-Engine,  114. 
Floating  Bodies,  75, 76. 
Flute,  142. 
Fog,  330. 
Foot-Pound,  31. 
Force,  kinds  of,  19,  20. 

represented  by  lines,  23. 

composition  and  resolution  of,  26 

correlation  of,  34. 
Fountains,  72. 
Freezing,  227. 

expansion  by,  226. 
Friction,  laws  of,  57,  58. 

friction  essential,  58. 
Frost,  330. 

6. 

Galvanometer,  290. 
Gases,  definition  of.  14. 
chapter  upon,  95. 


Gases,  compressibility  of,  95. 
Geissler  Tubes,  312. 
Governor,  240. 
Gravity,  15. 

laws  of,  35. 

centre  of  gravity,  36. 

H, 

Hail,  334. 
Halo,  195. 

Hardness,  test  of,  12. 
Harmonics,  248. 
Harmony  in  sound,  156. 
Hearing,  limits  of,  132. 
Heat,  chapter  on,  213. 

cause  of,  213. 

sources  of,  213. 

transmission  of,  230. 

mechanical  equivalent  of,  215. 

conduction  of,  234. 
Helix,  29. 

High- Pressure  Engine,  238. 
Horse-Power,  31. 
Hydraulic  Ram,  90. 
Hydraulics,  83. 

Hydrometers,  and  how  to  make  them,  79. 
Hydrostatics,  63. 
Hydrostatic  Bellows,  70. 
Hydrostatic  Press,  65. 
Hygrometer,  328. 


Images,  173. 
Inclined  Plane,  55. 
Indestructibility  of  matter,  9. 
Indian  Summer,  329. 
Induced  Currents,  299. 
Induction,  246,  260. 
Inertia,  15. 

examples  and  experiments,  16. 
Insulators,  electrical,  259,  262. 
Interference  of  waves,  water,  87. 

of  sound,  139. 

of  light,  200. 

Intermittent  Springs,  117. 
Isothermal  Lines,  325. 


K, 


Kaleidoscope,  172. 
Key-Note,  153. 
Knee-Joint,  27. 


INDEX. 


349 


Lens,  convex,  182. 

concave,  183. 
Lever,  three  kinds  of,  47. 

law  of,  48. 
Leyden  Jar,  269. 
Light,  chapter  on,  162. 

velocity  of,  167. 

reflection  of,  169. 

refraction  of,  177,  180. 

dispersion  of,  188. 

polarization  of,  202. 
Lightning,  272,  275. 
Lightning-Rods,  276. 
Liquids,  definition  of,  14. 

chapter  upon,  63. 

flow  of,  through  pipes,  85. 

rise  to  a  level,  72. 

incompressibility  of,  63. 

pressure  of,  on  bottom,  67. 

pressure  of,  on  sides,  69. 

pressure  upward,  70. 
Locomotive,  240. 


Machines,  47. 

create  no  power,  59. 
Magnet,  244. 

poles  of,  245. 
Magnetic  Storms,  293. 
Magnetism,  chapter  on,  244. 
Magneto-Electricity,  304. 
Manometric  Flames,  147.  . 
Mariotte's  Law,  95. 
Mass,  12. 

units  of,  13. 
Matter,  definition  of,  7. 

properties  of,  9-15. 
Mechanical  Powers,  47. 
Melodeon,  141. 
Meteorology,  319. 
Metric  System,  13,  343. 
Microscope,  205. 
Mirage,  187. 
Mirrors,  170. 

concave,  172. 

convex,  175. 
Mobility,  15. 
Molecules,  7. 

size  of,  8. 

motions  of,  14. 
Momentum,  21,  34. 


Monsoons,  337. 
Motion,  kinds  of,  19. 

Newton's  three  laws  of,  20. 
Mouth-Organ,  141. 
Music,  150. 
Musical  Sound,  129. 


Needle,  magnetic,  252. 

Nodes,  144. 

Noise,  definition  of,  129. 


0. 


Opera-Glasses,  207. 
Overtones,  146. 

P. 

Parallelogram  of  forces,  24. 
Pascal's  Vases,  68. 
Pendulum,  laws  of,  44,  45. 

for  clocks,  46. 
Perpetual  Motion,  59. 
Phonograph,  128. 
Photometry,  166. 
Piano,  139. 

not  a  perfect  instrument,  155. 

range  of,  133. 
Pipe-Organ,  141. 
Polarization  of  light,  202. 
Polygon  of  forces,  25. 
Pores  found  in  all  matter,  9, 10. 
Primary  Colors,  198. 
Projectile,  path  of,  42. 
Projecting  Lantern,  208. 
Pulley,  53. 
Pump,  the  common  one,  111. 

force-pump,  113. 

rotary  pump,  114. 


Radiant  Matter,  16, 313. 
Radiation  of  heat,  231. 
Rain,  333. 
Rainbow,  193. 
Reflection  of  light,  169. 

total  reflection,  179. 
Refraction  of  light,  177,  180,  187. 

law  of,  177. 
Refraction  of  sound,  128. 


30 


350 


INDEX. 


Resolution  of  forces,  26. 
Resonance,  127, 137. 
Resonator,  146. 
Resultant  of  forces,  24,  25. 
Rivers,  velocity  of,  86. 
Ruhmkorff  Coil,  309. 


Scale  in  music,  150. 
Screw,  57. 

Secondary  Battery,  287. 
Shadows,  164. 
Signal  Bureau,  341. 
Siphon,  115. 
uses  of,  116. 
experiments  with,  117. 
Siren,  130. 
Snow,  333. 

Solids,  definition  of,  14. 
Sonometer,  133. 
Sound,  chapter  on,  120. 
sound  a  vibration,  120. 
velocity  of,  in  the  air,  123. 
velocity  of,  in  solids  and  liquids,  123. 
loudness  of,  cause,  124. 
affected  by  conditions  of  the  atmos- 
phere, 125. 
refraction  of,  128. 
pitch  of,  130. 
character  of,  147. 
Sounding-Boards,  136. 
Sound-Waves,  length  of,  133. 
Speaking- Trumpets,  124. 
Speaking-Tubes,  124. 
Specific  Gravity,  definitions,  78. 
table  of,  345. 

to  find  specific  gravity  of  solids,  78. 
to  find  specific  gravity  of  liquids,  79. 
to  find  specific  gravity  of  gases,  80. 
Specific  Heat,  219. 
Spectroscope,  190. 
Spectrum  of  light,  189. 
Spherical  aberration,  187. 
Spirit-Level,  74, 
Sprengel's  Air-Pump,  109. 
Springs,  72. 
Stability,  38. 
Steam,  229. 
Steam-Engine,  237. 
Stereoscope,  208. 
Storms,  338. 


Suspension-Bridges,  material  of,  12. 
Sympathetic  Vibrations,  135. 


T, 

Telegraph,  294. 

Telephone,  302. 
Telescopes,  206. 
Temperament,  154. 
Temperature,  cause  of  change,  323. 
hottest  and  coldest  mouths,  325. 
Tenacity,  11. 
Tension  of  gases,  95. 
Thermal  Electricity,  299. 
Thermometer,  216. 
Thunder-Storms,  339. 
Timbre  of  sound,  148. 
Triangle  of  forces,  25. 
Twilight,  176. 

V. 

Vapors,  95. 
Vibrating  Strings,  laws  of,  134. 

vibrations  of,  in  parts,  143. 
Violin,  139. 
Voice,  human,  142. 

number  of  vibrations  in,  133. 
Voltaic  electricity,  278. 
Volume,  definition  of,  12. 


W. 

Water-Level,  74. 
Waves  in  water,  86. 

of  sound,  121. 

of  light,  163. 

of  heat,  213. 

interference  of,  87. 
Water- Wheels,  87. 

overshot-wheel,  88. 

breast-wheel,  88. 

undershot,  89. 

turbine,  89. 

Weather  Indications,  342. 
Wedge,  56. 
Weight  caused  by  gravity,  14. 

how  it  varies,  15. 
Wells,  72. 

Wheel  and  Axle,  51. 
Whispering-Galleries,  126. 
Winds,  cause  of,  335. 
Wind-instruments,  141. 


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the  stand-point  of  the  higher  analysis, 
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geometrical  discoveries  of  the  present 
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